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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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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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Different coupling between discrete energy states and reservoir

In this paper (arxiv version), in the middle portion of the image below, it's showing how the excited state is more strongly coupled to the electron reservoir (lead) than the ground state. (I don't ...
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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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Questions with Instanton Approach to Euclidean Path Integral

I'm reading through a section from Altland's and Simons' book on Condensed Matter Field Theory, and ran into a section I'm having trouble with (section 3.3 p. 115-117 if you have it, otherwise I try ...
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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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Quantum Tunneling in Molecular Magnets

An article on Quantum Tunneling of Magnetization in Single Molecule Magnets states that there can't be any tunneling between two orthogonal states and they didn't provide any explanation for this. ...
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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(...
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How to derive the Gamow complex energy?

Consider the following potential It was shown how to derive the complex energy (near the ground energy) of a resonance in the left well from the Euclidean path integral by Callan and Coleman, see ...
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Quantum Tunneling, Superposition, and The Uncertainty Principle

After looking through various papers and articles on explanations of quantum tunneling I've been left wondering about one thing. I've read explanations of tunneling as an affect of a particles wave ...
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Does quantum tunneling depend on insulator material?

Correct me if I am wrong,electron position is random on small scales,it can be described as wave function with certain probability distribution curve,I think its gaussian/bell shaped? Due to this ...
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With such a low mass, how do enzymes use quantum tunneling to lower the activation energy in a reaction

The Sun uses quantum tunneling to create nuclear fusion, but only can achieve this through it's large mass. So how can enzymes in our body achieve this feat?
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How do enzymes use quantum tunneling (also, please use relatively simple vocabulary)? [duplicate]

I already know how the Sun uses quantum tunneling to create nuclear fusion, but can't apply it to enzymes. Also, since I'm only in eighth grade, please use relatively simple language. Thanks!
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How is the needle/tip of an STM actually made?

I was wondering how the needle/tip of an STM is made. Any links would be also great, I couldn't find any.
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Dirac Delta potential

As we know a particle in attractive Dirac delta potential has discontinuity in the derivative of its wavefunction. I have two questions in this regard: Can a second order differential equation be ...
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How a tunnelled wave has the same energy even when the amplitude is lower

As I know that amount of energy carried by a wave is related to the amplitude of the wave than how in quantum tunnelling, tunnelled wave have the same energy even they have lower amplitude. I am ...
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Calculating the probability of transmission of a wave function between two delta distributions

Given is the potential :$V(x) = \frac{-\hbar^2}{m}D\delta(x+a) - \frac{-\hbar^2}{m} D\delta(x-a)$ with $a >0$ and $ D > 0$. A stream of particles from the positive $x$-axis are falling towards ...
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Chances of tunneling increased at low temperatures? [closed]

I have been giving a formula which states that the wavelength increases when the temperature decreases. When I plug this into the formula for the wavelength of Broglie, I get that my momentum ...
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Quantum Tunneling

Does Quantum tunneling prove there is a chance of big bang after the heat death of the universe? I mean how can we say it can produce another Big Bang in some years.
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Quantum tunnelling near the speed of light [closed]

Given a particle travelling very close to the speed of light encountering a barrier, is it possible for the particle to exceed the speed of light by tunnelling forward in the direction of motion ...
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Probability, tunnelling and transmission ratio [closed]

This question is about tunnelling. It is from Physics for the IB diploma book. The question introduces this graphWhere it is said the graph does not take reflected electrons into account and that the ...
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Specifics of the current flow in a tunnel diode

Those are two diagrams depicting current flow along with equivalent band diagrams form two different textbooks. I believe one first one is resonant diode and second is tunnel diode only. From the ...
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Rectangular Potential Barrier: Particle stuck in Barrier

I am thinking about a problem in quantum mechanics. Given a rectangular potential barrier, say the potential $U(x) = V$ for $0 < x < L$ and $U(x) = 0$ otherwise, I found the solution for the ...
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Will the electrons flowing in a metal wire come out of it and even through non conducting insulation outside it due to quantum tunneling?

Lets imagine that electrons are passing through a conducting wire. According to quantum mechanics , each electron is in form of wave function . Does that wave function have a value above 0 even ...