Questions tagged [quantum-tunneling]

Quantum tunneling is a classically-forbidden quantum effect that allows a bound object with energy less than the boundary to penetrate it with a small probability. A notable example is $\alpha$-decay

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Find the time $t$ such the initial wave packet just finished interaction with potential barrier [closed]

The initial wave form is the Gaussian () , and it interacts with a potential barrier given by V(x)={ -1 ,0<x<1 and 0 everywhere else . I want to know the time at which the wave finishes ...
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Pertubation Theory

For long-range barrier tunneling, consider three qubits governed by the Hamiltonian $H$. $$ H = -J(\sigma_1^+\sigma_2^-+\sigma_1^-\sigma_2^++\sigma_3^+\sigma_2^-+\sigma_3^-\sigma_2^+)+\frac{U}2\sigma^...
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Nuclear reactions in stars: tunneling?

Energy production in stars occurs mainly when a nucleus absorbs a proton or fuses with another nucleus. Some examples: (i) $\rm{p}(\rm{p},\rm{e}^+\nu)\rm{d}~$ and $~\rm{d}(\rm{p},\gamma)^3\rm{He}~$ ...
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Quantum Tunneling and Negative Kinetic energy

I don't understand how a particle can exist with negative kinetic energy. Consider this scenario: Here, an electron is tunneling through a potential barrier (The total energy of the electron is less ...
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Derivation of tunneling transmission probability using WKB approximation method

The transmission coefficient of tunneling particles throw the potential barrier $U(x)$ can be computed using WKB approximation method giving, $$T(E)=exp\Big(-2\int_{x_1}^{x_2}{dx\sqrt{\frac{2m}{ℏ^2}[U(...
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Understanding conductivity at nanoscale and validity of Ohm's law

Nanoparticles such as gold and silver are becoming more and more used to print circuit or enhance electrical properties of another material. But I have not been able to find sources that clarify how ...
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Conservation of energy in quantum tunneling

By this question, a particle can tunnel to inside a potential barrier. One aspect of this process that was not addressed in the answers was the conservation of energy. Motivated by this question, I am ...
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How particles can be found in classically forbidden regions? [duplicate]

If the total energy of the particle is less than the height of potential well. What could be interpretation that the particle can be found outside the well.
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Does the wavelength of an individual quantum particle affect its chances of quantum tunneling through a barrier?

I've read elsewhere about the energy of a wave or wave packet, and the amplitude of its probability amplitude, affecting its odds of quantum tunneling... But what about the wavelength or frequency of ...
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Transmission coefficient of a Gaussian wave packet through a potential barrier

I have simulated the scattering of a gaussian wave packet with a potential barrier (Crank-Nicolson), and through many simulations I have determined the dependence of the transmission coefficient with ...
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Tunneling effect - causes

I'm currently studying QM, and in my class tunneling effect was mentioned, but with no details. I was wondering what exactly causes this effect? Is this due to the wave characteristics of the particle,...
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Blocking quantum effects

A Faraday cage blocks electromagnetic fields, provided they are not intense enough to change the state to something non-conductive (e.g. slicing it in two with a laser). Is there any analogous system ...
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Can current and voltage be linked by an uncertainty relation when electrons tunnel through a barrier?

Quantum tunneling has been shown to be linked to uncertainty relations for some observables involved in the system. For instance, if we consider electrons tunneling through a potential barrier it can ...
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Why does quantum tunneling increase de-broglie wavelength?

The picture (taken from a textbook) shows how quantum tunneling occurs with electrons. Why does the de-Broglie wavelength of the electron change when doing this? It does not make intuitive sense to ...
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Why does the sun have the Fe?

I read the information about 'Abundance in the sun for the elements'. There are a lot of elements in the Sun. I thought 'how is it possible to exist Fe, Au, and so on in the Sun ?', but I couldn't ...
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Quantum Tunneling in Dirac Delta potential

In quantum mechanics phenomenon of tunneling is well understood ; we know that there is some finite probability to find the particle in classically forbidden region but potential of this forbidden ...
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Why does single electron Coulomb blockade charging use $Q^2/2C$?

Classically stored energy of a capacitor is $\frac{Q^2}{2C}$. However, the difference in energy when a single electron travels across the gates should be $qV$ But in couloumb blockade calculations, ...
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Is it possible to explain the Quantum tunneling with the uncertainty principle?

I'm a high school student in South Korea(It is my first English question ever). I found descriptions of quantum tunneling with the uncertainty principle in Korea. There are two kinds of descriptions ...
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How can quantum tunnelling be applied to the penetration/reflection of electromagnetic waves?

I am trying to use quantum mechanics to explain the penetrating power of electromagnetic radiations through, say, a thin sheet of glass. I imagine the glass to be a one dimensional potential "wall". $$...
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Invisible walls paradox in quantum mechanics

Background Quantum mechanics considers only electromagnetic interactions. This fact might be a jut obscured in the introductory texts, but all the potentials in discussions of scattering, tunneling, ...
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Tunneling of electrically neutral objects [closed]

The question is motivated by a joke-question posted in this forum, but it is serious: How would we calculate the tunneling probability for a multi-particle/multi-atom object with zero net charge? The ...
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Is a 3-terminal magnetic tunnel junction possible?

I am wondering, whether a 3 terminals magnetic tunnel junction can be implemented, as shown in the figure below. At the bottom I have a normal metal (NM), on the top - a magnetic junction (FM = ...
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Black Hole Escape By Quantum Tunneling

The first minute of this explanation: https://youtu.be/ZgOhQhpoczs about Black Hole evaporation (Hawking Radiation) talks about particles with de Broglie wavelengths bigger than the Event Horizon. ...
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How fast does a particle need to go to have a significant probability to quantum tunnel through a star?

According to this answer tunneling probability depends, among other things I don't know, on the length of the barrier. Due to length contraction when going at relativistic speeds, it seems it should ...
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Quantum tunneling probablity w.r.t. harmonic differences corresponding to nearby potentials

Simplest case I can think of: Consider 2 neighboring square energy wells. One of them is occupied with a particle at ground state and has length L, the other is unoccupied and has a length 2L/3. In ...
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Can quantum tunneling decrease entropy?

I was wondering this. What if particles tunnel to a lower entropy state? Then can that actually decrease entropy, if every particle in the universe so happens to tunnel in a certain way? Or is this ...
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Tunneling in quantum mechanics

We have this well known case of ~4.2 MeV α-particle being emitted from the U-238 nucleus but the α-particle emitted from the Po-212 which has the energy of ~9MeV cannot penetrate it. This phenomenon ...
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Tunneling of electrons in a metal junction

If a metal of two different chemical potential are placed together, thermodynamics tells us that electron will flow from higher to lower chemical potential to reach an equilibrium. But it is not ...
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Quantum configuration of a Zener diode

What would be the potential for a charge carrier in a Zener diode? I'm trying to motivate its ability to tunnel given a high enough voltage gradient... Would it merely be something like an infinite ...
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Electron tunneling: transmission>1? [duplicate]

Assume a simple electron tunneling scheme from medium 1 into medium 2. By applying the boundary conditions (continuity of the wave function and its derivative at the interface), it is straightforward ...
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Quantum tunneling, how to graph a T(E) transmission over energy function for a potential barrier diagram

So, I have these 2 potential barrier diagrams for particles coming from the left, and my exercise is too graph corresponding T(E)graphs in detail taking into consideration what new effects that can ...
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Escape a black hole by tunneling faster then the speed of light [closed]

I do understand that nothing can escape a BH (not particles, no information), and this question is not about why you cannot escape. This question is not about Hawking radiation, and I do understand ...
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Question about tunneling and energy

So I am in my course of physical chemistry and in my book there is this image. And quite frankly i am struggling to understand it. I believe i understand the liquid drop model. This is supposed to ...
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What do you see in 'A Boy and His Atom'

A boy and his atom is a short movie by IBM animated by actually moving atoms around and using a scanning tunneling microscope to display the result. When I first saw this picture I was fascinated ...
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What happens in an infinitely long potential step when $E<V$?

In the case of a potential step when $E<V$, the transmission coefficient of the particle is zero. However, there is also an exponentially decaying wavefunction of the particle in that classically ...
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Energy eigenfunctions of a truncated harmonic oscillator-like potential

Assume a potential of the form \begin{eqnarray}V(x) &=& \frac{1}{2}m\omega^2x^2,~-x_0\leq x\leq x_0,\\&=& 0,\hspace{2.5cm}{\rm otherwise} \end{eqnarray} where $x_0$ is a finite ...
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Is this a possible interpretation of quantum tunneling?

Suppose we have a particle in a finite potential well where the potential is $V_0$ and the ensemble average momentum is $\langle p\rangle$, so that the average kinetic energy $$\langle T\rangle =\frac{...
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Quantum tunneling of dark energy from black holes

There was an article posted recently suggesting there is a very deep connection between dark energy and black holes. https://phys.org/news/2019-09-black-holes-dark-energy.html I was thinking this ...
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Equilibrium points of bounce/instanton solution after Wick's rotation

In Coleman's paper Fate of the false vacuum: Semiclassical theory while working out the exponential coefficient for tunneling probability through a potential barrier, he studies the problem with Wick'...
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Has many-body tunneling at the level of nuclei been studied?

In a recent paper, the authors stress the difference between single-body tunneling and many-body tunneling (at the atomic level): "In contrast to the well-studied incoherent single-particle tunnelling,...
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Why doesn't the amplitude of a wave-function fall off to zero immediately at a potential barrier?

When a wave function in QM potential well problems interact with a potential barrier with height more than the energy of the wave, the amplitude of the wave doesn't immediately falls off to zero, ...
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What is in physical term meaning of penetration of a potential barrier?

While solving the quantum mechanical case of potential barrier meaning - $$\text{E} <\text{V} $$ The transmission coefficient is nonzero. My problem is what is happening with particle motion Has ...
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What is the real difference between tunneling ionization and multiphoton ionization (MPI)?

Ionization is when an EM neutral atom gaing Em charge by losing or gaining an electron. Tunnel ionization is ionization due to quantum tunneling. In classical ionization, an electron must have ...
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Allowed energies for a particle inside potential barrier

The allowed energies for a particle inside a potential well are discrete ones, and for a particle outside the well, the energy specrum is continuum. But what for a particle inside a potential barrier? ...
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Simultaneous eigenstates of Hamiltonian and momentum operator

Given the potential barrier, \begin{align} V(x, y) = \left\{ \begin{array}{cc} V_{0} & \hspace{5mm} \text{if $0 \leq x \leq D$} \\ 0 & \hspace{5mm} \text{...
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Does the internal state of a particle change after tunneling?

Consider a toy 1-dimensional model molecule: two particles with positions $x_1$ and $x_2$ and the same (for simplicity) masses, attracted to each other by a harmonic potential $$U(x_1-x_2)=U_0 (x_1-...
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Tunnelling of a gaussian wavepacket through a potential barrier compared to the free case

I am studying numerical methods for solving the time-dependent Schrödinger equation and simulated the tunnelling of a gaussian wavepacket through a potential barrier. During the simulation I keep ...
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Quantum tunneling through the event horizon (EH): Is the EH a potential barrier for Quantum tunneling?

This is not a duplicate. I am not asking whether anything can escape a BH, I understand nothing can. My question is whether the potential barrier in the definition of Quantum tunneling can be a BH EH? ...
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Quantum mechanical tunneling - example from Mcintyre's book

Can someone explain what he means here: "because the electrons inside the two materials have lower potential energy than they would in the free space between them due to the work ...
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Quantum Tunneling and Conservation of Energy

According to my understanding quantum mechanics, the probability of any particular particle in the universe being at any specific location in the universe is very small but never actually becomes zero....

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