What is Quantum Tunneling, Exactly?

Summary

In this video, Jade dives into the fascinating concept of quantum tunneling, addressing viewer questions from a previous video about the Schrödinger equation. She explains how, unlike classical physics, quantum particles like electrons can sometimes 'tunnel' through barriers despite lacking the energy to do so. Drawing comparisons to light waves and evanescent waves, Jade explores the probabilistic nature of quantum physics, breaking down complex ideas in an approachable way. She also discusses the limitations of the 'particle in a box' model and promotes Brilliant.org as a resource for learning quantum mechanics.

Takeaways

• 🧲 Quantum tunneling allows particles like electrons to pass through barriers even when they lack sufficient kinetic energy.
• 🌊 Quantum mechanics is probabilistic, unlike classical physics, which allows for the possibility of particles being in multiple places at once.
• 📏 The Heisenberg Uncertainty Principle states that the exact position and momentum of a particle cannot be simultaneously known.
• 🌌 A wave function is used to represent the probability of finding a quantum particle like an electron in a certain location.
• 💥 When a wave function encounters a barrier, it can reflect and form an evanescent wave, which is key to quantum tunneling.
• 💡 The phenomenon of total internal reflection in optics, where light is completely reflected within a medium, leads to the formation of evanescent waves.
• 🔍 An evanescent wave is a small wave that decays quickly and is usually not detectable, but it's crucial for quantum tunneling.
• 🔗 Frustrated total internal reflection occurs when an evanescent wave doesn't decay to zero before reaching another material, allowing it to continue.
• ⚛️ Quantum tunneling plays a significant role in various physical processes, including nuclear fusion, DNA mutation, and scanning tunneling microscopy.
• 📚 Understanding quantum mechanics requires not just knowing the concepts but also working through the mathematical equations to gain intuition.
• 🎓 The script promotes Brilliant.org as a resource for learning quantum mechanics through interactive quizzes and courses.

Q & A

What is quantum tunneling?

Quantum tunneling is a phenomenon in quantum mechanics where a particle like an electron can pass through a potential barrier, even if it doesn't have enough energy to overcome it. This occurs due to the probabilistic nature of quantum particles, which allows a small probability that the particle can 'tunnel' through the barrier.

How is quantum tunneling different from classical physics?

In classical physics, if an object (like a ball) doesn't have enough kinetic energy to overcome a barrier (like a hill), it remains stuck. However, in quantum mechanics, even if a particle lacks sufficient energy to cross the barrier, there is still a small chance it can tunnel through it due to its wave-like behavior.

What is the role of the wave function in quantum mechanics?

The wave function in quantum mechanics represents the probability distribution of a particle's location. Instead of having a fixed position, the particle's position is spread out like a wave, and the wave function gives the likelihood of finding the particle at different locations.

What is an evanescent wave, and how does it relate to quantum tunneling?

An evanescent wave is a rapidly decaying wave that appears at the boundary of a material when light or a quantum particle reflects off it. In quantum tunneling, the electron's wave function decays exponentially at the barrier, similar to an evanescent wave, and if the barrier is thin enough, the wave can continue on the other side, allowing tunneling to occur.

Why can't an electron escape from an infinite potential well?

In an infinite potential well, the walls are infinitely high and thick, meaning that the probability of the electron tunneling through them is zero. The wave function decays completely before reaching the other side of the barrier, making tunneling impossible.

How does the Heisenberg Uncertainty Principle relate to quantum tunneling?

The Heisenberg Uncertainty Principle states that we cannot know both the exact position and momentum of a quantum particle at the same time. This uncertainty allows quantum particles like electrons to behave probabilistically, enabling phenomena like tunneling where the electron has a small but nonzero chance of being found on the other side of a barrier.

What is frustrated total internal reflection, and how is it similar to quantum tunneling?

Frustrated total internal reflection occurs when light reflects off a boundary but some of the evanescent wave interacts with a nearby material and continues through. This is similar to quantum tunneling, where an electron’s wave function decays at a barrier but continues if the barrier is thin enough.

Why is the wave function treated like a real physical wave in quantum mechanics?

The wave function is treated like a real physical wave because its behavior, such as reflection, interference, and tunneling, can be modeled accurately by wave mechanics. Even though scientists are still unsure whether the wave function represents a real physical entity or is just a mathematical tool, it behaves in a way that aligns with wave-based phenomena.

Why is it important to understand the math behind quantum mechanics?

Understanding the math behind quantum mechanics is crucial because it provides a deeper, more intuitive grasp of the principles governing quantum phenomena. Solving equations like the Schrodinger equation helps build this understanding, as it reveals how quantum particles behave under different conditions.

How does quantum tunneling play a role in real-world phenomena?

Quantum tunneling is essential in various real-world processes, such as nuclear fusion in stars, where particles tunnel through energy barriers to sustain the fusion reaction. It also plays a role in DNA mutations and is utilized in scanning tunneling microscopy, which allows for imaging surfaces at the atomic level.

Outlines

00:00

🔬 Introduction to Quantum Tunneling

The paragraph introduces the concept of quantum tunneling, starting with a discussion on the Schrodinger equation from a previous video. It addresses questions about the possibility of electrons tunneling outside a box, despite classical physics suggesting otherwise. The explanation begins with a comparison to a ball stuck at the bottom of a hill, unable to climb over without enough kinetic energy. Quantum tunneling is then introduced as a quantum mechanical phenomenon where particles like electrons can sometimes pass through potential barriers even if they lack the energy to overcome them. The paragraph emphasizes the probabilistic nature of quantum physics, contrasting it with classical physics, and introduces the Heisenberg Uncertainty Principle. It explains how the position of an electron is described probabilistically by a wave function, which is a central concept in understanding quantum tunneling.

05:04

🌌 Quantum Tunneling Explained

This paragraph delves deeper into quantum tunneling by using the analogy of light waves and their behavior at boundaries. It discusses how light can refract and reflect when passing from one medium to another, and how total internal reflection occurs at a certain angle. The concept of the evanescent wave, which is a small wave that forms at the boundary and decays exponentially, is introduced. The paragraph explains how this phenomenon is crucial for understanding quantum tunneling. It suggests that when an electron, represented as a wave, encounters a barrier, an evanescent wave is formed. If the barrier is thin enough, part of this wave can tunnel through to the other side, indicating a small but non-zero probability of finding the electron beyond the barrier. The paragraph also clarifies a previous statement about an electron in a box, explaining that in the context of an infinite potential well, tunneling is not possible due to the infinitely high walls. The summary concludes with a recommendation to explore further through interactive learning platforms like Brilliant.org, which offers courses on quantum mechanics, and a call to action for viewers to engage with the content and series.

Keywords

💡Schrodinger equation

The Schrodinger equation is a fundamental equation in quantum mechanics that describes how the quantum state of a physical system changes over time. It is a partial differential equation that is central to the video's discussion on quantum tunneling. The video mentions that the equation is used to analyze the behavior of an electron in a box, and how it relates to the probability of finding the electron outside the box, which is zero in an infinite potential well scenario.

💡Quantum tunneling

Quantum tunneling is a quantum mechanical phenomenon where a particle passes through a potential barrier even though it seemingly lacks the energy to do so classically. The video uses the analogy of a ball and a hill to explain that, unlike classical physics, a quantum particle can 'tunnel' through a barrier. This concept is crucial for understanding phenomena like nuclear fusion and scanning tunneling microscopy.

💡Classical physics

Classical physics refers to the laws of physics that describe the behavior of matter and energy at a scale where quantum effects are negligible. In the video, classical physics is contrasted with quantum physics to highlight the limitations of classical mechanics in explaining phenomena like quantum tunneling, where a ball without enough kinetic energy cannot get over a hill.

💡Heisenberg Uncertainty Principle

The Heisenberg Uncertainty Principle states that it is impossible to simultaneously know the exact position and momentum of a particle. This principle is fundamental to quantum mechanics and is mentioned in the video to explain why we can't pinpoint the exact location of an electron, but only its probable location.

💡Wave function

A wave function in quantum mechanics is a mathematical description of the quantum state of a system. The video uses the wave function to illustrate the probabilities of where an electron might be found, which is key to understanding how an electron can tunnel through a barrier despite not having enough energy to overcome it.

💡Probabilistic

In the context of quantum mechanics, 'probabilistic' refers to the nature of quantum systems where the outcomes are described in terms of probabilities rather than certainties. The video emphasizes this by stating that quantum physics is probabilistic and uses wave functions to model these probabilities.

💡Evanescent wave

An evanescent wave is a wave that dies out, or decays, exponentially with distance. In the video, the concept of evanescent waves is used to explain how a small part of a wave can 'tunnel' through a barrier, which is central to the quantum tunneling phenomenon.

💡Total internal reflection

Total internal reflection is a phenomenon in optics where light is completely reflected back into the original medium when it strikes a boundary at an angle greater than the critical angle. The video uses this concept to explain how light can create an evanescent wave at the boundary, which is crucial for the discussion on quantum tunneling.

💡Frustrated total internal reflection

Frustrated total internal reflection occurs when an evanescent wave at the boundary of two materials does not decay to zero before reaching the second material, allowing it to continue propagation. The video mentions this as a real-world example of how evanescent waves can be observed, which relates to the quantum tunneling of particles.

💡Infinite potential well

An infinite potential well is a theoretical model in quantum mechanics where a particle is confined within an area with infinitely high potential barriers. The video clarifies a misconception by explaining that the 'particle in a box' scenario is actually an infinite potential well, where the probability of finding a particle outside the well is zero, thus no tunneling can occur.

💡Brilliant.org

Brilliant.org is mentioned in the video as a learning platform that offers courses on quantum mechanics, including the Schrodinger equation. The platform is used as an example of where viewers can deepen their understanding of quantum mechanics through interactive quizzes and problem-solving.

Highlights

Introduction to the concept of quantum tunneling and its relevance to the Schrodinger equation.

Explanation of how quantum tunneling differs from classical physics through the analogy of a ball and a hill.

Description of the probabilistic nature of quantum physics and the Heisenberg Uncertainty Principle.

Introduction to the wave function as a model for the probabilities of an electron's location.

Discussion on how a wave function behaves when it encounters a barrier, including reflection and the concept of an evanescent wave.

Explanation of total internal reflection and the phenomenon of an evanescent wave in optics.

The role of Maxwell's equations in predicting the behavior of light and its connection to quantum tunneling.

Description of frustrated total internal reflection and its visual demonstration.

The significance of the evanescent wave in enabling quantum tunneling.

Clarification on the 'particle in a box' model and its infinite potential well assumption.

The practical applications of quantum tunneling in nuclear fusion, DNA mutation, and scanning tunneling microscopy.

The debate over whether the wave function is a mathematical tool or a real physical entity.

The importance of solving the Schrodinger equation to gain a deeper understanding of quantum mechanics.

Promotion of Brilliant.org as a learning platform with a focus on quantum mechanics.

Invitation for viewers to participate in community polls to influence video content.

Overview of the quantum physics series and where to find more information.

Transcripts

This episode is sponsored by Brilliant. Hi guys! Jade here. So a few weeks ago I

made a video on the Schrodinger equation and in it I said that if we place an

electron in a box the probability that it could be found outside the box is

zero, and a lot of you commented with questions like "oh but what about quantum

tunneling? Isn't there some cases where the electron can tunnel outside of the

box?", so I thought what the heck I'll just make a whole video about it. It's super

cool and I will answer that specific question at the end of the video, but

first, what is quantum tunneling? Well the short version is in regular classical

physics if you have a ball at the bottom of a hill, if it doesn't get a big enough

push to get over the hill it's kind of just stuck there. Putting this into

physics talk, if the ball doesn't have enough kinetic energy to get over the

potential energy of the hill, it'll never get over, like, ever. But of course, in

quantum mechanics things aren't so simple. If we replace the ball with a

quantum particle like an electron and the hill with some kind of potential

barrier, even if the electron doesn't have enough kinetic energy to jump the

potential barrier, sometimes it can end up on the other side. This is called

quantum tunneling and in this video we're going to see how it works. So now

the long version! So one of the biggest differences between quantum and

classical physics is that quantum physics is probabilistic. Unlike a ball

we can't pinpoint exactly where an electron is. This comes from the

Heisenberg Uncertainty Principle which says that we can never know the exact

position and momentum of an object. It's not because our measuring devices are

too crappy or because we're too slow, it's just something fundamental about

the laws of nature. But not all hope is lost! Maybe we don't know exactly where

the electron is but we know with a pretty high probability that it's around

here somewhere. We can actually model these probabilities with a wave or, more

technically, a wave function. This wavy cloud gives us the probabilities of

where the electron is likely to be, so now instead of imagining a particle

traveling toward a barrier, imagine a wave traveling toward a barrier.

Now when this wave collides with the barrier, because the electron doesn't

have enough kinetic energy to make it over, it gets reflected. But wait, what

about the whole tunneling thing? Well there's this secret property of waves

you probably didn't learn in school. Light is an electromagnetic wave so

let's imagine what happens when we shine a light beam through glass. When we shine

a light beam through a piece of glass, at the boundary where the glass meets the

air, the light beam will bend or refract. You may have noticed this effect if

you've ever looked at a straw in your water glass. The visual illusion comes

from the bending of light at the boundary of two different mediums, in

this case, air and water. But refraction isn't the only thing that can happen at

a boundary. Light can also get reflected. The amount of light which is reflected

and refracted depends on the angle that the light hits the boundary. All mediums

have a certain angle where 100% of the light beam is reflected. This is called

total internal reflection and you may have heard that when this happens 100%

of the incident beam goes back into the reflected beam, but that's not true.

These are Maxwell's equations and though they may look innocent they form the

entire foundation of classical electromagnetism. Remember how we said

that light is an electromagnetic wave? This means that the way light behaves in

different scenarios can be predicted and modeled by solving Maxwell's equations

now when we solve these equations for the case of total internal reflection we

get something very interesting this isn't that interesting instead of there

being an abrupt drop off where the light hits the boundary there's this very

quick exponential drop off this is shown by this term here I know this looks

super complicated and well it is so let's just get rid of all that

mumbo-jumbo here and just focus on the bit that matters this is a graph of e to

the power X which as you can see models exponential growth but the term in our

equation is e to the power negative which is simply the backwards version of

this exponential decay so we have this tiny little drop off wave here this is

called an evanescent wave which in my opinion is a very suitable name the word

evanescent means soon passing out of sight memory or existence quickly fading

or disappearing an evanescent wave is pretty much exactly what it sounds like

it decays incredibly quickly lasting only a few wavelengths before vanishing

so we can't usually see or detect it but if we place another material

sufficiently close to the boundary of the first sometimes the evanescent wave

doesn't decay completely to zero before hitting the next material so it can then

continue to travel onwards this is called frustrated total internal

reflection and I recommend looking up a demo on YouTube after this I would have

shown you in this video but for anyone who has read my Twitter bio you know

that experiments are not my forte I actually did try it and it just didn't

work my olds digression optics was one of my favorite subjects in university

and we did a lot of work on evanescent waves but I never really got a physical

intuition for why they're there the only answer I ever found is because Maxwell's

equations say so like when you solve the equations you end up with this decaying

exponential but other than that I can't really say a physical reason for why a

wave can't just abruptly stop at a boundary and change direction so if you

do please explain it to me in the comments ok digression over this wave

might be puny but it's the reason behind why quantum tunneling is possible

remember that we're trading our electron as a probability wave which means that

when it gets reflected here in evanescent wave forms at the boundary if

the barrier is thin enough sometimes some of the wave actually makes it

through so if some of the wave makes it through and this wave represents the

probability of the location of the electrons then there's some very small

but nonzero probability that our electron is over here even though this

probability is tiny because there are usually so many quantum particles

involved in any physical process the effects of Quan

tunneling a large enough to be essential to nuclear fusion in stars spontaneous

mutation in DNA and scanning tunneling microscopy it may seem stalling that

we're treating the wavefunction exactly like an electromagnetic wave it's hard

to imagine something so abstract like the probabilities of electron locations

as a real physical thing that travels and reflects and tunnels the truth is

scientists still don't know exactly what a wavefunction is they don't know

whether it's purely a mathematical tool we've created to help us predict things

about quantum objects or whether it's a real physical wave but what they do know

is that it can be modeled pretty much perfectly by wave mechanics when we

solve the Schrodinger wave equation for the electron inside the barrier we get

this exponential decay which is exactly what we would expect of an evanescent

wave speaking of Schrodinger's equation in my video about that I said if we

place an electron in a box the probability that it could be found

outside the box is zero and a lot of you are confused because what about

tunneling well the truth is I didn't specify this very well in a lot of

university degrees a particle in a box is the simplest case we use to analyze

Schrodinger's equation but it's actually a particle in an infinite potential well

so instead of this being a box look at it as a well with infinitely high and

thick walls in tunneling the barrier needs to be thin enough so that the

evanescent wave doesn't have time to completely decay to zero before reaching

the other side only then can it propagate onwards with infinitely high

and thick walls that's obviously impossible so yeah my bad didn't specify

infinity in my last video someone commented asking whether it was futile

to try and truly understand quantum mechanics without doing the math and my

immediate reaction was yes while you can learn the catchphrases and get an

overall gist of what's going on to really get that gut feeling of

understanding an intuition you need to work through the problems and see what

the equations tell you I didn't really understand the Schrodinger equation

until I solved it myself brilliant org is a learning website with

an entire course dedicated to quantum mechanics it starts with the very first

Berman's which reveals strange quantum behavior and takes you all the way to

shredding equation it has this interactive quiz style which I love

because you can work through problems at your own pace and check your

understanding at every step I actually just worked through these

quizzes on the mathematical foundations of quantum physics and had a few of my

own aha moments as some questions I'd had since University were finally

answered there are also tons of other courses specialising in math physics and

computer science brilliant is offering a 20% discount to the first 200 people to

sign up using this link just go to brilliant org slash up and Adam and

start learning quantum physics today thanks for watching guys I hope you

enjoyed the video it was actually the result of a poll I posted on the YouTube

community tab so if you would like to be included in those polls and vote on your

favorite topics then just click the notification bell this video is also

part of a quantum physics series I've got going on at the moment which I've

linked for you at the end of the video and in the description so until next

time bye