What is Quantum Tunneling, Exactly?
Summary
TLDRIn 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
🔬 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.
🌌 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.
Mindmap
Keywords
💡Schrodinger equation
💡Quantum tunneling
💡Classical physics
💡Heisenberg Uncertainty Principle
💡Wave function
💡Probabilistic
💡Evanescent wave
💡Total internal reflection
💡Frustrated total internal reflection
💡Infinite potential well
💡Brilliant.org
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
تصفح المزيد من مقاطع الفيديو ذات الصلة
What is The Schrödinger Equation, Exactly?
Particles and waves: The central mystery of quantum mechanics - Chad Orzel
Dr Quantum Double Slit Experiment
Waves: Light, Sound, and the nature of Reality
The Fourier Series and Fourier Transform Demystified
DUNIA QUANTUM EMANG AGAK LAIN!! TEMBOK SAJA BISA TEMBUS!!
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