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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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Why does the imaginary time Euler-Lagrange equation imply the potential goes to zero at infinite imaginary time?

On reading up about the bounce solution for false vacuum decay in S. Coleman's The Fate of the False Vacuum I it was stated that the equation $$0 = \frac{1}{2} \frac{\partial q}{\partial \tau} . \frac{...
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How can we calculate simple quantum tunneling processes from the path integral?

I've been reading through Altland and Simons' Condensed Matter Field Theory, and am confused a bit by their discussion on tunneling and instantons. However I don't quite understand how this relates to ...
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Best method for numerically solving Schrodinger equation for quantum tunneling w/ arbitrary potential

Goal: to compute accurate tunneling probabilities with an arbitrary barrier using numerical solutions to Schrodinger's equation. Main question: what method is best for generating a robust numerical ...
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The $\alpha$ particle's energy inside a nucleus is lesser than the Coulomb barrier height. Justify

The $\alpha$-decay is usually explained via quantum tunnelling. This is because the $\alpha$ particles do not have sufficient energy to climb over the Coulomb barrier. But how do we know this? We can ...
Solidification's user avatar
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Equation for probability of quantum tunneling

I am looking at fusion reactions in stars and came across how particles will bypass the Coulomb barrier through quantum tunneling. I was wondering if there is an equation for the probability of a ...
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Does quantum tunnelling have anything to with perception of light?

There have been studies suggesting that the sense of smell has something to do with quantum tunnelling but I'm afraid I don't know the exact details. Do we possess internal mechanisms that simply &...
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How to condition an STM tip?

I am starting work on an atomic force microscope and a scanning tunneling microscope and I wanted to ask for advice. How to proceed to get the sharpest tip and therefore the best resolution?
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Clarification on bound states: do "locally bound" states exist?

In Griffiths, a state with energy $E$ is said to be "bound" if $$E < \min\left(\lim_{x\to\infty} V(x), \lim_{x\to-\infty} V(x)\right)$$ (i.e. $E$ is less than both of those quantities). ...
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Why is probability outside the infinite square well zero? [duplicate]

In an infinite square well, potential energy is given below, why is the probability of finding a particle in the position of infinite potential energy zero? $$V(x)=\begin{cases} 0,& \text{if } ...
GedankenExperimentalist's user avatar
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How to compute the hopping matrix considering the change of multiple states?

My question is quite simple, but I couldn't find the answer anywhere. Hubbard Models usually have a hopping term as follow: $$H_{hop} = -t \sum_{<i,j>} \left( c^{\dagger}_{j} c_{i} + c^{\dagger}...
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Energy of electron during Tunnel ionisation

I have been studying an emission mechanism that exploits the ionization, disassociation and subsequent fluorescent recombination of nitrogen molecule by a femtosecond laser for velocimetry. The ...
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Are quantum tunneling slow down by time dilation affected? [duplicate]

If i setup to clock to work at the same rate at stationary. The first clock operated on quantum tunneling. Setup electron to tunneling and repel another electron. Which acts as sensor. The second ...
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Free particle encountering an infinite potential barrier

I understand that a wave function cannot penetrate through a barrier that has infinite potential. However when the wave function reflects off from the barrier what does this look like? If we're in a ...
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How to calculate the distance between the barriers in a double barrier heterostructure?

I know there is a peak in the current flowing through the heterostructure when the voltage bias applied $U$ equals 0.05 V. From what I know this should align with the energy being equal to that of the ...
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Current in a Superconducting Loop Interrupted by a Josephson Junction

Assuming we have the following circuit consisting of a superconducting loop having the same superconductor material everywhere, and interrupted by the short Josephson junction J1 with a phase ...
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Whats the relation between resonances observed in the transmission curve, and the density of states?

How are the oscillations observed in a T(E) curve related to the density of states? Do we observe the oscillations when there's a larger density of states at that particular energy?
star123's user avatar
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How can we use saddle point approximation for a bounce solution which is not even a strict local minimum of the Euclidean action?

In calculating the false vacuum decay, the main contribution to the imaginary energy part of the Euclidean path integral comes from the bounce solution. And we somehow apply saddle point approximation ...
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Gravity cause wavefunction collapse? (Roger penrose) [closed]

Roger Penrose suggested that gravity might play a role in the collapse of the wave function (which describes a system as a superposition of multiple values of Position, momentum etc.). According to ...
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Is it possible that when measured more than one Cooper pair will have tunneled across the junction?

If I've understood the idea correctly a charge qubit is formed by a superconducting island coupled by a Joseph junction to a superconducting reservoir. The state of the qubit is determined by the ...
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Can quantum tunneling of some sort allow 2 solids which dont touch each other to have the same chemical potential?

Suppose we have 2 solids seperated by a distance x.If the distance x is in the quantum range(10-20 atoms) even though the solids dont touch each other would their Fermi levels become the same after ...
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Moving Mott Transition Tunnels

I have a question on moving tunnels. Let's assume you have a wrapped semiconductor by a piezolectric material that creates a series of staggered mott transitions along the conductor. Each mott ...
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How do protons fuse in the sun?

I know that Nucelar fusion in the sun requires quantum tunneling to occur, as otherwise the Sun's core wouldn't be hot enough to overcome the Fusion barrier. However while the 2nd and further stage of ...
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How hot would the sun have to be to work without quantum tunnelling

I know that the Nuclear fusion in the sun would not work without quantum tunnelling, as the nuclei wouldn’t ever have enough energy to overcome the potential barrier. So how hot would the sun have to ...
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Zener diode reverse bias I(V) equation

What is the equation for the reverse bias current in terms of voltage applied? And this even be analytically derived? If so, how to derive it. I can't seem to find good resources on this topic.
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How does shape of a wavefunction changes as it encounters a potential barrier?

A particle of mass and energy $E > 0$ in one dimension is scattered by the potential below If the particle was moving from $x = -\infty$ to $x= +\infty$, which of the following graphs gives the ...
Dinesh Katoch's user avatar
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Why the wave function decays exponentially when it crosses the potential barrier?

That may be an obvious question, but I would like a physical answer, not math.
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Alpha decay must be quantum tunnelling. Why?

By measuring the energies of the emitted alpha particles, how can we say that they have energies less than the height of the nuclear potential well when they are inside the well? How can we be sure ...
Solidification's user avatar
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Can't find any QTC (quantum tunneling composite)

As per the title, I can't find any QTC to buy online. I may be dumb or just looking in the wrong places. Is it that uncommon? Are there any places that sell it locally in Melbourne, or is it just ...
honeywagon's user avatar
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3 answers
339 views

Why do we interpret transmission and reflection coefficients as probabilities?

In standard 1D textbook step potential problems, for $E>V_0$ with $V_0$ the step potential for $x>0$, one finds that for $x<0$ that eigensolutions are of the form $$\psi(x) = A_1e^{i\sqrt{2ME/...
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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 ...
Iv Nik's user avatar
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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 ...
Cartesian Bear's user avatar
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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 ...
Iv Nik's user avatar
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1 answer
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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. ...
Iv Nik's user avatar
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1 answer
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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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5 votes
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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 ...
user333905's user avatar
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2 answers
118 views

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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1 answer
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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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Has quantum tunnelling of an atom ever been empirically confirmed?

The phenomenon first drew attention in the case of alpha decay, in which alpha particles escape from certain radioactive atomic nuclei. But has scientists ever observed quantum tunnelling of an atom? ...
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Why doesn't environmental decoherence completely prevent from happening the quantum tunnelling of macroscopic objects? [duplicate]

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 ...
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