Quantum tunneling Definition and 131 Threads

Quantum tunnelling or tunneling (US) is the quantum mechanical phenomenon where a wavefunction can propagate through a potential barrier.
The transmission through the barrier can be finite and depends exponentially on the barrier height and barrier width. The wavefunction may disappear on one side and reappear on the other side. The wavefunction and its first derivative are continuous. In steady-state, the probability flux in the forward direction is spatially uniform. No particle or wave is lost. Tunneling occurs with barriers of thickness around 1–3 nm and smaller.Some authors also identify the mere penetration of the wavefunction into the barrier, without transmission on the other side as a tunneling effect. Quantum tunneling is not predicted by the laws of classical mechanics where surmounting a potential barrier requires potential energy.
Quantum tunneling plays an essential role in physical phenomena, such as nuclear fusion. It has applications in the tunnel diode, quantum computing, and in the scanning tunneling microscope.
The effect was predicted in the early 20th century. Its acceptance as a general physical phenomenon came mid-century.Quantum tunneling is projected to create physical limits to the size of the transistors used in microelectronics, due to electrons being able to tunnel past transistors that are too small.Tunneling may be explained in terms of the Heisenberg uncertainty principle in that a quantum object can be known as a wave or as a particle in general. In other words, the uncertainty in the exact location of light particles allows these particles to break rules of classical mechanics and move in space without passing over the potential energy barrier.
Quantum tunnelling may be one of the mechanisms of proton decay.

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  1. Tertius

    I Tunneling with Gaussian Wave Packet

    The goal is to have accurate 1D numerical results for tunneling probabilities through an arbitrary barrier without relying on analytic approximations such as WKB. If there is a more ideal approach to this, I am happy to change tactics. Time independent, for example, but I am not sure how to...
  2. Tertius

    Correct Setup for Finite Difference to Calculate Quantum Tunneling

    I thought I solved the problem in answering my own post a few days ago, but the tunneling probability vs. energy trend is clearly wrong. I've remade the post because I have totally changed my approach and need a better understanding of the boundary setup. Overall description: a plane wave...
  3. Tertius

    Numerical Solution to Schrodinger Equation w/ Coulomb Potential

    I am doing this to have my own solution for customization and understanding. I also want to manually check the WKB approximation accuracy at various energies against this static solution. I've split the problem into 3 regions and am solving it in 1D, but am having problems with how to define...
  4. K

    B Question about Hawking Radiation and Iron Stars

    So, I was thinking, the most massive black holes are expected to evaporates in roughly a googol year. Fine. But I was reading that if protons are stable, every planet and non black hole star remains are basically expected to turn into iron star from quantum tunneling after mind numbing time on...
  5. A

    I Looking for resources about tunneling effect on two delta functional barriers

    Hello. I have 2 questions. First, I've read theory of tunneling effect but I need theory of two and more delta functional barriers. How do you think where can I read more about it? I need it for superconductors. And second, where can I find how to add magnetic field to theory of it? How it...
  6. Kinker

    I Does gravity cause quantum decoherence?

    Does gravity cause quantum decoherence? In the microscopic world, gravity seems to act weakly, but in the macroscopic world, it seems to act strongly. Is this the boundary between the microscopic world and the macroscopic world? So a phenomenon like quantum tunneling can occur in the microscopic...
  7. Kinker

    B Does decoherence prevent 100% of quantum tunneling of macro object?

    Isn't the quantum tunneling probability of macroscopic objects always zero due to quantum decoherence? It may be possible in the microscopic world, but I always think it is impossible in the macroscopic world due to countless interactions. Isn't this the same in a universe with infinite time...
  8. Addez123

    Confused about quantum tunneling through 200V not eV

    I have the equations to calculate transmission probability, my problem is that the barrier is given in Volts not electron volts. $$200V = e \cdot 200 eV = 3.2 \cdot 10^{-17} eV$$ I am not even sure if that's a correct conversion. But if it is then this "barrier" is extremly small and 99.999%...
  9. Samama Fahim

    Limits of Integration in the Transmission Coefficient

    Initially '0' is the upper limit and ##a = \frac{Ze^2}{E}## is the lower limit. With change of variable ##x = \frac{Er}{Ze^2}##, for ##r=0##, ##x=0##, and for ##r=\frac{Ze^2}{E}##, ##x=1##, so 1 should be the lower limit. However, he takes 1 as the upper limit, and without a minus sign. Why is...
  10. M

    Quantum Tunneling to an infinite wall

    I have the equations for all three regions but usually for region 3, which is Ce^ikx+De-ikx, the C term would be zero since there is no reflection, but with the infinite wall would it reflect? Would the whole wavefunction go to zero like when working with the infinite square wall? I'm stuck on...
  11. A

    I Superluminal Quantum tunneling without FTL messaging

    I recently viewed a PBS "Space time" video The video references two articles of which one is paywalled while the other is not. https://iopscience.iop.org/article/10.1088/1367-2630/abb515/pdf https://www.nature.com/articles/s41586-020-2490-7?proof=tIn the discussion section of the free article...
  12. Wannabe Physicist

    Exploring the Time-Energy Uncertainty Relation to Solve a Schrodinger Equation

    I am guessing time-energy uncertainty relation is the way to solve this. I solved the Schrodinger equation for both the regions and used to continuity at ##x=-a, 0,a## and got ##\psi(-a<x<0) = A\sin(\kappa(x+a))## and ##\psi(0<x<a) = -A\sin(\kappa(x-a))## where ##\kappa^2 = 2mE/\hbar^2##...
  13. The Baron

    I Could Light Absorption Be Linked to Quantum Tunneling?

    Hi, I have just now started learning about quantum mechanics, and I have an Idea, which i am 99 percent sure is wrong, but i wanted to post it just in case. Okay, so I researched it a little and it turns out that the probability for a single particle to experience quantum tunneling is 0.1%...
  14. B

    B Sun powered by quantum tunneling - question

    I recently found out that for nuclear fusion to occur the temperature needs to be around 100 Million Kelvin and that the hottest part of the sun is only at 27 Million Kelvin. And that the reason nuclear fusion is occurring in the sun is because of quantum tunneling—allowing a very small fraction...
  15. J

    I Quantum Tunneling in an STM: ELI5 Requested

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  16. J

    I Quantum Tunneling in the Sun and Conservation of Energy

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  17. wolfy

    What Prerequisites do I need in order to understand Quantum Tunneling?

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  18. Superposed_Cat

    I Pair production via Quantum Tunneling has negative Kinetic energy?

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  19. wolfy

    B Quantum Tunneling different individual transmission probabilities

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  20. N

    I Is it possible to explain Quantum tunneling with the HUP?

    I'm a student in South Korea(It is my first English question ever). I found descriptions of quantum tunneling explained by the uncertainty principle in Korea. There are two kinds of descriptions to explain quantum tunneling; position-momentum and time-energy uncertainty principle. First...
  21. mgkii

    Frustrated Total Internal Reflection

    I've been reading into - and watching videos on - FTIR as an explanation of Quantum Tunnelling. The articles and videos I've watched switch between classical and quantum systems so frequently its left me with a question I can't find an answer to - the texts that seem like they might answer it...
  22. T

    Quantum tunneling: T(E) graph for a potential barrier diagram

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  23. S

    I Understanding Electron Behavior in Quantum Tunneling through Dielectrics

    When an electron leaves a conductor and tunnels through a thin dielectric; how does it behave in the space occupied by the dielectric? Does it behave like a ballistic electron traveling through vacuum? Is it instead that the electron never really occupies the space in the dielectric?
  24. YoungPhysicist

    B White dwarf quantum tunnelling

    I just finished watching the video "The Last Light Before Eternal Darkness – White Dwarfs & Black Dwarfs" At 5:17 he mentioned quantum tunneling will take up a timespan so long that calling it forever is ok. But nothing takes forever,so,how long will it actually take? ps:I later realized...
  25. A

    I How Long Does a Particle Stay in a Quantum Potential Well?

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  26. SameerTahir

    I Source of energy for quantum tunneling of a particle

    If a micro-particle tunnel through a barrier which has higher potential energy than the energy of the particle, then from where does the particle get the energy to cross that barrier?
  27. E

    Probability of penetrating a potential barrier

    Homework Statement The probability for a particle of energy E<<V0 to penetrate a potential barrier of height V0 and width d is approximately \frac{16E}{V_0}exp\left[\frac{-2d\sqrt{2m(V_0-E)}}{\hbar}\right]. An electron moves between two potential barriers of height V0 and 2v0 that are of widths...
  28. SameerTahir

    I Concepts to understand Quantum Tunneling

    What concepts should be cleared to better understand quantum tunneling?.
  29. PGaccount

    B Quantum Tunneling: Reflection and Transmission Probabilities Explained

    (P1 + P2)2 - 4P1P2 = (P1 - P2)2 (A - B = C) The reflection and transmission probabilities are R = C/A T = B/A Can one understand this from the first equation? ----[
  30. N

    I Quantum Tunneling Max Distance

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  31. Ethan Singer

    I (Conceptual) Infinity energy via quantum tunneling & Nuclear Fusion?

    I was unsure whether or not to post this question here or in the Nuclear physics sub-section, but it's a relatively simple question: Given that quantum tunneling exists, would it be possible to produce infinite energy via repeated nuclear fusion reactions? Now given the second law of...
  32. Scott_10438

    Equation for plasma wave/light speed travel?

    Hi guys I'm finishing up some promo art for my original comic book. You're seein it here first. But its missing something- an appropriate equation. I would like to integrate a math equation into the art. I am attempting to depict FTL travel, using qualities similar to an LWFA, the plasma being...
  33. J

    B Quantum tunneling - Questions about some pop-science claims

    This might become a series of questions, but let me begin with the most essential one. According to QM/QFT, would it be true that there is a non-zero chance for an object on Earth to instantaneously tunnel to the moon for example? Like let's say a paper with a note on it. Could this paper...
  34. A

    I Quantum "tunneling" of sorts and QFT....

    Hi all, Another naive question related a previous post (where the topic diverged somewhat). I'm wondering about the following thought experiment: Consider the field associated with a single electron. Now, confine the field to a region (volume) of radius R - that is, field values outside of R...
  35. T

    I Quantum Tunneling: Can it Cause Stable Systems To Transition?

    I have noticed that quantum tunneling can cause unstable systems to suddenly transit to a stable state without going through its energy barrier. Can quantum tunneling cause stable systems, with as low energy as possible, to transit to other states?
  36. G

    How Does Quantum Tunneling Affect Electron Confinement in Potential Wells?

    Homework Statement An electron with a total energy of Eo = 4.4 eV is in the potential well shown above. 1) Find the ratio of the wavelength in Region III to the wavelength in Region I. λ III / λI = 1.772) Given that the wave function of the electron vanishes at the left boundary of Region...
  37. R

    I How does nucleation work in cosmology?

    In this article https://en.wikipedia.org/wiki/False_vacuum#Bubble_nucleation it says that "In the theoretical physics of the false vacuum, the system moves to a lower energy state – either the true vacuum, or another, lower energy vacuum – through a process known as bubble nucleation." What is...
  38. R

    How does Nucleation work? Relationship with vacuums?

    What is nucleation and how it works? In cosmology, which is the relationship that nucleation have with quantum tunneling, vacuums and Big Bang?
  39. R

    B Exactly how quantum tunneling leads to a Big Bang?

    In wikipedia says that in a big amount of time quantum tunneling can create a new Big Bang. EXACTLY, how this happens. https://en.wikipedia.org/wiki/Future_of_an_expanding_universe ("Beyond" part) *note: I'm in high school, but feel free to explain this with complicate process.
  40. N

    I Please help me understand quantum tunneling conceptually?

    Hello, in my intro to quantum class, we recently started the chapter on quantum tunneling. While I understand the math, I don't understand conceptually what is going on. I do have my thoughts on the matter, but I am not sure that they are correct. I have a few questions: 1) Is the de Broglie...
  41. Ranku

    I Electroweak symmetry breaking and quantum tunneling.

    Does electroweak symmetry breaking involve quantum tunneling?
  42. Ranku

    I Quantum tunneling in symmetry breaking

    Does electroweak symmetry breaking involve quantum tunneling, just like GUT symmetry breaking?
  43. N

    I Problem of quantum tunneling and Many Worlds interpretation?

    On wikipedia it says that MWI doesn't explain quantum tunneling well. "A tunnelling particle would have more energy than what is actually measured in experiments." What do you guys think?
  44. C

    I Are we in a simulation and quantum tunneling?

    Preface: As I understand it, according to quantum mechanics, there is a very good probability that I am sitting right in my chair right now, typing this question out. However, there is a non-zero, ever so small probability, however infinitesimally small chance that I am somewhere else in the...
  45. durant35

    I Can Quantum Tunneling Cause Objects to Instantly Swap Places?

    Hello guys, I have few questions about the well-known quantum tunneling. I'll start off with the animation from wikipedia So question #1 why doesn't the barrier collapse the wave function, is that even possible? What's the difference between the barrier and the measurement screen in double...
  46. Alan Ezra

    I The barrier length in quantum tunneling

    Hi, In transmission coefficient T= exp(-2sqrt(2m(U-E)/hbar^2)L), L, as I interpret it, is the distance of the potential barrier. I am wondering if I have N particles all with kinetic energy E, approaching the barrier, can I integrate the transmission coefficient over a distance from infinity to...
  47. G

    Quantum tunneling instantaneous

    http://m.phys.org/news/2015-05-physicists-quantum-tunneling-mystery.html Does this mean that the tunnelling time was actually zero, and the electron 'skips' over the gap, or does it mean that the electron wave traveled at the speed of light followed by an instantaneous jump later on
  48. P

    Quantum Tunneling of a conduction electron in Copper

    Homework Statement A conduction electron moves through a block of Cu until it reaches the surface. At the surface the electron feels a strong force exerted by the nonuniform charge distribution in that region. This force tends to attract the electron back into the metal which is what causes the...
  49. sevenperforce

    Event horizon and quantum tunneling

    It's been a while since I took any QM so I'm fairly rusty...not even sure that I'm asking this in the right way. How does one set up the equations to determine the characteristics of quantum tunneling if you have a particle with a particular energy inside an event horizon? For example, suppose...
  50. J

    Pilot wave theory and quantum tunneling

    Just a question about pilot wave theory as an alternative to SQM. Researchers in ANU have recently shown that quantum tunnelling of a particle through a barrier is instantaneous. Does this finding verify the Copenhagen superposition interpretation of QM and at the same time invalidate the...
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