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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For a particle in a 1D box, what is the expectation value of momentum for a particle that has tunnelled through the walls and escaped?

For a particle in a box, where the walls of the box have a finite (i.e. not infinite) potential energy, what is the expectation value of the momentum of a particle which has tunnelled through the wall ...
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What are the exact relations between bound states, discrete spectra, and negative energies in quantum mechanics?

Consider the nonrelativistic quantum mechanics of one particle in one dimension ("NRQMOPOD") with the time-independent Schrodinger equation  \left( -\frac{\hbar^2}{2m} \frac{d^2}{dx^2} + V(...
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Reverse bias p-n junction diode and Kinetic energy

In reverse bias p-n junction diode, which energy is lower than the energy of the potential barrier: the average kinetic energy of the would-be-tunnelling electrons or the kinetic energy of the ...
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Quantum tunnelling of an electron in ground state

I asked my question on Quora and i got various conflicting answers. So, I decided that here I could get a definite answer. Unless the question is not too vague. According to quantum mechanics, is ...
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Tunnelling explained by time-independent Schroedinger equation

I am a retired theoretical physicist. I am currently trying to promote the exact sciences by helping highschool students with their mathematics, physics and chemistry studies. One student, who is in ...
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WKB approximation derivation for $E<V$

I understand that we can write any complex wavefunction on polar form $A\exp(iθ)$ with both $A,θ$ real. Following the logic of Griffiths on WKB (here, page 291): We write the energy wavefunction in ...
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In reverse bias p-n junction diode, how do one know that the kinetic energy of the tunnelling electron is lower than the energy of the barrier? [duplicate]

In reverse bias p-n junction diode, how do one know that the kinetic energy of the (thermally generated in the p-side) tunnelling electron is actually lower than the energy of the barrier (the ...
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What happens step-by-step (and why) when a particle tries to escape an infinite potential well?

I am aware that the following question might be quite elementary. My background is mainly in mathematics and my physics education is limited to high-school level material (discounting analogues made ...
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In the Esaki diode, how can one be 100% sure that there are tunnelling electrons with lower energy in comparison with the barrier's energy?

In the tunnel diode, if it is all about the statistical accumulation/distribution, how can one be certain that there are electrons with lower energy (in comparison with the barrier's energy) which ...
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In the Esaki diode, how do physicists measure/estimate the velocity of a would-be-tunneling electron?

Layman's explanation, please. Let's consider an Esaki diode. How do physicists measure/obtain the velocity of a would-be-tunneling electron in order to justify the claim that the potential barrier is ...
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Is there real physical possibility for a "macroscopic" object to undergo quantum tunnelling? [duplicate]

According to quantum mechanics, there is fantastically (astonishingly, astronomically, infinitesimally, ridiculously etc.) small probability for a book on a table to quantum tunnel through the table. ...
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Will the probability for tunnelling go completely to zero? [closed]

According to quantum mechanics, the probability for quantum tunnelling (of an object) never become completely zero, no matter how "big" is the height and the thickness of the barrier. ...
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Zener breakdown - a quantum mechanical derivation

In §6.8 of Ziman's "Principles of the Theory of Solids" he derives the imaginary component of the wave vector of an electron inside an energy gap (due to action of an electric field). He ...
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Electronic tunneling between two states

I am reading Steering Electrons on Moving Pathways (Beratan et al. 2009) which is about electron tunneling in biomolecules, and specifically the processes via which an electron can move from an ...
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Can a particle experience tunneling even if its energy is higher than the barrier? [closed]

I know that quantum tunneling can make particle go through the barrier even when its energy is not enough, but dose it happen when the particle's energy is higher than the barrier? Will it go through ...
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How to Understand Quantum Phase Slips in Josephson Junction Array in terms of Tunneling?

I am trying to understand quantum phase slips in terms of quantum tunneling between the minima of the Josephson potential (see page 2 right before equation (1)). Consider the following circuit diagram ...
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Why is there non-zero probability for a particle to "escape" completely from a solid? [closed]

Let's consider a particle (electron or proton) in a "macroscopic" solid. Outside of the solid, the state of the particle would have a higher energy. Because of the conservation of energy, ...
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Molecules are made up of numerous subatomic particles, so don't they constantly interact? How can we achieve quantum coherence? ($\rm C_{60}$)

Since $\rm C_{60}$ is a molecule made up of numerous subatomic particles, no matter how separated from the environment, the interaction between $\rm C_{60}$'s subatomic particles inevitably causes ...
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What would be a probability of a silicon atom from the moon to quantum tunnel to earth?

What is the probability of a silicon atom going from the moon and landing on the Earth? The reason is that there is a barrier that the silicon atom has to cross which is the moon's own gravity so that ...
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A macroscopic object has the order of Avogadro’s number of particles. That’s over $10^{23}$. So the probability of all of them tunneling, at the same time, is on the order of that original small ...