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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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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Chiral tunnelling in graphene

I am trying to reproduce the results of this paper: Chiral tunnelling in single and bilayer graphene. I have done all the math but I couldn't figure out how the $s(=sgn(E))$ and $s'(=sgn(E-V_0))$ ...
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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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Why do quantum tunneling consume energy, if not then why it must pay back borrowed energy quickly? [duplicate]

I understand that quantum tunneling is a pure example of the uncertainty principle but clearly transistor had to be powered to work properly, anyhow I like to know if it is true that particle must ...
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Why wavefunction becomes exponentially smaller during quantum tunneling?

I am interested in quantum tunneling and I am wondering why the wavefunction of a particle would becomes smaller so that there is a slight possibility of finding it at the other side of a big energy ...
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Electron Tunneling

An electron dot is a Quantum confinement where the motion of the electron is constrained in all the three dimensions ,which means that the electron has zero potential energy and supposed to be at rest ...
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Tunneling of Electrons

I just have a hypothetical question: If we have two beams of electrons which have the same energy, they approach some potential barrier of same fixed height. One of the barriers have a width of $d$ ...
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How does quantum tunneling work in a bigger mass?

im trying to figure out the probability of a 9 y/o kid going right through an object. im trying to do this with a compacted form of schrodingers equation: e^(-2*(m*v/H/2pi)*l) where l = 22,34mm, h = ...
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Can a quark quantum tunnel outside a nucleus?

I read that a particle wavefunction can extend over a thin barrier and there is a probability of finding it over the barrier even though it doesn't have the necessary energy, what about quark?
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WKB connection formulae from the path integral

The semiclassical, or WKB, approximation is one that is far more natural in the path integral formalism than it is when derived from the Schrodinger equation directly. Furthermore, the connection ...
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Can I consider electron scattering with grain boundaries in metal as a tunneling process?

I am reading about the Mayadas-Shatzkes model (MS model). when electrons are scattered with the grain boundary, there is a probability that it will be transmitted to the other side of the grain ...
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In aluminum, how does electricity travel through the surface oxide layer?

Suppose I connect a conductive wire (cross section 1 mm$^2$) to an aluminum object. Since aluminum is highly conductive, electricity will flow smoothly inside the object with little resistance. ...
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1D Potential Barrier Boundary Conditions (tunneling)

I'm trying to solve the boundary conditions of a 1D potential barrier for a free particle. The boundary conditions on the continuity of the wave function and its first derivatives leads to four ...
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Quantum tunneling into a black hole

The currently accepted answer to Throwing a micro black hole into the sun: does it collapse into a black hole or does it result in a supernova? states that a small black hole of mass approximately $10^...
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Is there any connection between instantons and surface-interacting polymers?

Excluded volume polymers interacting with a penetrable hypersurface of variable dimension is a very interesting system to study critical behavior via perturbative renormalization. Since a penetrable ...
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Quantum Mechanical Tunneling in a Resonant Tunneling Diode

I am currently trying to simulate a Resonant Tunneling Diode (RTD) on a somewhat basic level, so the question is rather general. Quantum-mechanically its structure is shown well in this figure: Two ...
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Could false quantum vacuum decay change fundamental laws of physics? [closed]

It is often said that low energy/effective physical laws (i.e fundamental physical constants) could possibly change if a quantum false vacuum decays into a true (stable) level of quantum vacuum. But, ...
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Why can't a particle penetrate an infinite potential barrier?

I am studying basic quantum theory. My question is: Why can't a particle penetrate an infinite potential barrier? The reasoning that I have applied is that particles under consideration have finite ...
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Mathematical Proof of Decay in Tunneling with tunnel lenght L

Let us suppose we have a particle with energy $E$ and $E<U$ and the potential defined as $U(x)=0$ for $x<0$ (I) $U(x)=U_0$ for $x>L$ (III) and $U(x)=U$ for $0<x<L$ (II) I find ...
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What happens when an electron, or a neutron, approaches a brick wall?

(I have looked through 100 questions tagged quantum tunneling before asking) I know how to calculate quantum tunneling for a single particle in a given potential energy landscape in single-particle ...
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Time-dependent Quantum step potential: Short-time tunneling possible?

Consider the Schrödinger equation $i \partial_t \psi(x,t) = -\frac{\hbar^2}{2m} \Delta \psi(x,t) + V(x) \psi(x,t) + W(t) \psi(x,t)$ where $\psi(x,t)$ is the wave function, $m$ the particle mass and $...
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Many-body quantum tunneling: Is quantum tunneling sensitive to decoherence?

If we have a many-particle System that is strongly correlated, the tunneling probability can significantly increase; see this article here: https://www.sciencedaily.com/releases/2014/06/140612142215....
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Quantum tunneling/transmission through an infinite potential

In Shankar exercise 5.4.2 we consider the reflection and transmission of a wavefunction through a delta potential $V(x) = aV_0\delta(x)$. I understand that to mean that the potential is zero ...
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Quantum tunneling in the context of quantum annealing

I understand the concept of tunneling only from a very basic particle encountering a barrier point of view. If I have a finite square barrier of energy height $D$, I expect classically no probability ...
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Could electrons with a certain wavelength pass through a hole, or chamber, smaller than their wavelength? [duplicate]

I always thought, an electron could not pass through a hole, with a diameter, which is smaller than its wavelength. Just like microwaves could not pass through a metal mesh with small holes, but ...
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Quantum tunnelling, energy conservation

If we allow that the energy to allow quantum tunnelling through a potential barrier has been borrowed by the Heisenberg energy-time uncertainty relation, from the vacuum energy. How is the borrowed ...
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Has quantum tunneling to iron been observed?

Earlier this year, I saw the video mentioned in another question, and then another one by someone else (earlier this week on PBS Space-Time) on the same subject. That second video said the quantum ...
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Tunneling junction in electromagnetic field [closed]

Why in presence of electromagnetic field hamiltonian,describing 2 systems with tunneling(for example josephson junction ) $$H=H_L+H_R+T(I+I^{\dagger})$$ where $I=c_Lc^{\dagger}_R$ is tunneling ...
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What happens if we detect an electron in a place with higher potential than the wavefunction has energy?

A wavefunction has a particular energy and is spread over space. For example, an electron in the ground state (n=1) in hydrogen has an energy of -13.6 eV, but its possible that we measure the ...
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Vacuum Stability

I am studying one of the paper of Sidney Coleman, "Fate of the False Vacuum. II. First quantum corrections". Just before eq. (2.18) he says "Because of time translation invariance, this equation ...
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given an AC field, how many photons are there?

Say you are applying a time varying potential across double quantum dots in the form of $V_{ac}$cos($2\pi f t$). We know that each photon has an energy $E_{photon}= hf$. Is it correct to say that ...
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Quantum coherence Lasers

If the photons of a laser beam all are coherent so that they all have the same momentum why don't we see them tunnel barriers very often ? Maybe I am misunderstanding what the coherence in laser beam ...
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Link between tunneling rate and conductivity

Generally speaking, in the theory of single-electron tunneling events (one electron tunneling through a quantum well), the rate under which this event occurs is calculated using Fermi's Golden Rule, ...
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If a nucleus is radioactive, will another nucleus with lesser binding energy be necessarily radioactive?

Consider two nuclei A and B. Let the binding energy of A is less than the binding energy of B (i.e., A is unstable compared to B) and B is known to be radioactive. Does it mean that A also has to be ...
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What are the differences and similarities between dynamical tunneling and quantum tunneling?

In case of a double well potential, particle can tunnel from one well to another and this process is known as quantum tunneling or tunneling in general. I want to know about dynamical tunneling and ...
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Quantum tunneling versus over-the-barrier ionization

I was doing a quantum physics past paper and there was this question about ionizing atoms with laser. My answers made reference to the photons within the laser knocking off or transferring their ...
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Does a wave function never reach zero probability density?

$$ψ=e^{iκx}$$ Since the wave function is an exponential equation, is there no point with zero probability density of finding a given particle? Does that justify quantum tunneling?
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What's the largest possible particle/atom that can experience quantum tunneling?

Quantum tunneling occurs when the energy state of a particle gets sufficiently high. Does this mean that particles traveling at relativistic speeds are more likely to experience this phenomena? Is ...
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What happens if particle is measured outside finite well? [duplicate]

A particle, which is in bound state (and eigenstate) of a finite well, has a small probability of being found just outside the well. If one happens to locate it there, then to the experimenter how ...
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Schroedinger equation on the line with non-symmetric double well potential

In the 3rd volume of the Landau-Lifschitz text book ("Quantum mechanics") problem 3 after section 50 studies the Schroedinger equation on the line with symmetric double well potential, e.g. $U(x)=g(x^...
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Validity of the thin wall approximation

Inspired by the question How can I understand the tunneling problem by Euclidean path integral where the quadratic fluctuation has a negative eigenvalue?, I decided to come back to the first paper by ...
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Physical intuition for the Wilczek-Parikh tunneling picture of Hawking radiation

There's a naive pop-sci explanation of Hawking radiation, where a particle-antiparticle pair is produced just inside the event horizon. The particle with positive energy tunnels out and escapes, while ...
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Why can't the probability distribution of a quantum particle tunnelling be normalized?

Consider a quantum particle moving in the $x$- direction and hitting a wall of higher energy than it has. Classically, the particle cannot pass through the wall. Quantum mechanically, it can. Let $u(...