Quantum tunneling Definition and 130 Threads

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...

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...

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...

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...

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...

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...

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...

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%...

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...

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...

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...

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##...

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%...

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...

In an STM, you image the surface topography by tunnelling electrons from the metallic tip to the conductive surface, while measuring the current. I have worked with these instruments before and I never understood why does one need a quantum explanation for this. Wouldn't the electron jump to...

Hi, In my textbook it says that if you consider the electrostatic repulsive barrier that protons in the Sun need to overcome in order to get into the range of the strong nuclear force to fuse together then it fails to fully account for the measured power output of the Sun. It says that the...

Summary:: What tools like Calculus, Algebra, etc do I need to Understand how to Write a Quantum Tunneling Equation? I am New to QM however I feel I may have what it takes to do the Math, however, I am not privy to what the Prerequisites are that are needed to perform the...

If we have a photon being converted to a positron-electron pair, but we lack enough energy for this to happen (hv<2Me*c^2) but the difference is smaller than the uncertainty amount, such that tunneling may be possible, would the resultant pair have net negative energy? Would tunneling even be...

I have gone through all the videos on Youtube about Quantum Tunneling and became interested in it, so any helpful feedback would be appreciated. Do all the different individual transmission probabilities of electrons, protons, and such remain constant? May I ask what is the "formula" or...

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...

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...

This is the V(x) diagrams and what I am thinking (really not sure though) is that for the first one you the energy has to reach V2 before it can start transmitting and the graph can take off from T=0, since there is an increase in energy potential that is V2. And as the energy increases, the...

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?

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...

Let's suppose I have a potential well: $$ V(x)= \begin{cases} \infty,\quad x<0\\ -V_0,\quad 0<x<R\\ \frac{\hbar^2g^2}{2mx^2},\quad x\geq R \end{cases} $$ If ##E=\frac{\hbar^2k^2}{2m}## and ##g>>1##, how can I calculate how much time a particle of mass ##m## and energy ##E## will stay inside...

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?

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...

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

(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? ----[

I was assuming that it is possible to repeatedly measure an electron's position, but that it was not possible to know the result of the subsequent measurement because of the uncertainty principle. What I was wondering was whether the maximum distance between the two measurements is limited by...

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...

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...

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...

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...

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?

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...

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...

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

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...

Does electroweak symmetry breaking involve quantum tunneling?

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

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?

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...

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...

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...

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

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...

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...

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...