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13
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7answers
3k views

Can a particle be *physically* observed inside a quantum barrier?

I understand that a particle approaching a finite potential barrier with $E < V_0$, there still is a probability of finding the particle on the other side of the barrier due to quantum tunneling. ...
11
votes
5answers
1k views

Is there a classical analog to quantum mechanical tunneling?

In comments to a Phys.SE question, it has been written: 'Tunneling' is perfectly real, even in classical physics. [...] For sufficiently large temperatures this can put the system above a hump in ...
11
votes
1answer
389 views

Hawking Radiation as Tunneling

Firstly, I'm aware that Hawking radiation can be derived in the "normal" way using the Bogoliubov transformation. However, I was intrigued by the heuristic explanation in terms of tunneling. The ...
10
votes
1answer
254 views

Probability conservation in WKB tunneling

Suppose we have quantum mechanical plane waves of energy $E$ incident upon a one-dimensional potential barrier $V(x)$ with sloping sides. One can compare the WKB solutions in the three relevant ...
9
votes
3answers
701 views

Is quantum tunneling related to imaginary time?

I was studying for my exam and looking at the chapter which talks about Potential-energy graphs. Let's take this as an example: My book states that: "If the object is in $B$ and has a total energy ...
9
votes
1answer
280 views

Does tritium hydride exhibit measurable spontaneous fusion via proton tunneling?

In a fascinating 30 June 2013 article in Nature Chemistry, researchers from the University of Leeds found that when molecules of hydroxyl (OH, a fairly stable radical) and methanol (CH$_3$OH) are cold ...
7
votes
4answers
5k views

Tunneling v. Hopping

Can someone explain the difference between hopping and tunneling? The context I'm considering is conduction in semiconductors, specifically between impurity states within the bandgap. It's always ...
7
votes
1answer
340 views

Understanding multiple instanton contributions to vacuum tunneling in a double potential well

I'm trying to understand the method of calculating the transition probability of one vacuum state to another in a double well potential, using instantons. The reference I am following is Sidney ...
7
votes
2answers
381 views

Is there a time delay during tunnelling?

A particle hitting a square potential barrier can tunnel through it to get to the other side and carry on. Is there a time delay in this process?
6
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3answers
1k views

Why is tunneling not a classical idea?

There is no tunneling in the case of infinite potential barrier, but there is when we have a finite well. In the classical analog, in the first case we have a particle bouncing between to infinitely ...
6
votes
2answers
3k views

Tunneling of alpha particles

Consider this explanation of the alpha decay: It says The Coulomb barrier faced by an alpha particle with this energy is about 26 MeV, so by classical physics it cannot escape at all. ...
5
votes
2answers
304 views

Quantum barrier for photons [closed]

In quantum mechanics, a particle may tunnel through a barrier it would not be able to surmount in a classical sense. My question is this: What are all the factors that may prevent a photon from ...
5
votes
1answer
482 views

Chance of “macro tunneling”?

We know that subatomic particles can and do tunnel through barriers, so it is theoretically "possible" somewhat that a grain of sand could tunnel through a paper, but Id like to get some perspective ...
5
votes
1answer
271 views

Hawking Radiation from the WKB Approximation

Reading this paper which is itself an exposition of Parikh and Wilczek's paper, I get to a point where I fail to be able to follow the calculation. Now this is undoubtably because my calculational ...
5
votes
1answer
430 views

Quantum tunneling effect in a potential of the kind $V(x)=A\frac{x^2}{1+x^4}$

Given a potential: $$V(x)=A\frac{x^2}{1+x^4}$$ with $A\gt 1$ and a quantum particle inside the well around the point $x=0$. I'm stuck on the calculation of the transmission and reflection coefficients ...
4
votes
4answers
705 views

Where is the particle during a tunneling event?

If, say, a particle with energy $E<V_0$, approaches a finite potential barrier with height $V_0$, and happens to tunnel through, where would the particle be during the time period when it is to the ...
4
votes
2answers
148 views

Can Half Lives (hypothetically) be Measured by Wave-functions?

I understand that half-lives are measured over several days/months/years of observing a certain amount of an element and seeing how long it takes to decay a certain amount, but I'm curious as to ...
4
votes
2answers
563 views

How much time does it takes an electron to tunnel through a barrier?

I know that in quantum mechanics there is no "time operator", so such a question is ill-posed. Anyway if the tunneling is instantaneous, this would imply an information transmission faster than $c$. ...
4
votes
2answers
254 views

What was the largest object/particle tunneling observed?

What is a current record? Reference to that would be nice. and what can be expected in near future? what are the theoretical limits?
4
votes
1answer
322 views

Does tunneling transmission probability depend on the density of states or velocity?

In some quantum text books [1], the tunneling transmission formula depends only on the density of states of 2 regions (DOS) involved in tunneling. ($T(E) = C \times DOS_1(E) \times DOS_2(E)$, where C ...
3
votes
1answer
162 views

How can I understand the tunneling problem by Euclidean path integral where the quadratic fluctuation has a negative eigenvalue?

I came across the S. Coleman's seminal papers 'Fate of the false vacuum' (http://dx.doi.org/10.1103/PhysRevD.15.2929, http://dx.doi.org/10.1103/PhysRevD.16.1762) where he describes the tunneling ...
3
votes
2answers
724 views

What's the difference between hopping and tunneling?

My professor made a distinction between electron hopping (the closest wikipedia had an article on) and tunneling, saying that one (he didn't say which, but I assume hopping) was temperature dependent ...
3
votes
3answers
303 views

Why do tunneling photons outrace their non tunneling counterparts in vacuum?

If we describe a photons with a wave packet, moving towards a potential barrier and E smaller than V, there is a finite chance that it will tunnel to the other side. In this process it is likely that ...
3
votes
1answer
171 views

Refraction: Energy flow, tunneling and Evanescent EM waves

In the full internal reflection case where we have a refracted evanescent wave, If another object is nearby, then we could have wave tunneling phenomenon(frustrated total internal reflection). I am ...
3
votes
4answers
301 views

Virtual particles/quantum tunneling - conservation of energy?

I'm confused as to how the above phenomena can take place since arent they breaking the law of conservation of energy (even, if temporarily)?
3
votes
0answers
87 views

Tunneling from Dirac material into Schrodinger material?

When a Dirac material, like graphene or TI, has a connection with a normal metal which Schrodinger equation govern on their carriers, how could we manipulate the tunneling of electron from Dirac side ...
3
votes
0answers
97 views

The relation between the action of tunneling and the energy

In the semi-classical physics, the probability of the penetration through a barrier is given by $$ p \sim \exp \left( - A_{0} (E) \right), $$ where $A_0$ is the imaginary part of the action and $E$ ...
2
votes
3answers
77 views

Why do wider double wells have a lower $\Delta E$ than thinner ones?

In this diagram, in which an $n=1 (E_{1})$ and $n=2 (E_{2})$ wave have been superimposed, the probability density of the new, combined wave changes with time. The period of its shifting density is ...
2
votes
2answers
162 views

Why does transmission probability decrease, increase, then decrease again?

We did a quantum tunneling lab online. We used a Java program to model the electron wave function and show what happens when there is a step potential (U is less than E). Our value for the ...
2
votes
2answers
152 views

Why a tunnel diode (TD) is called a diode?

Traditionally, a diode is a 2-terminal device that limits current to flow in one direction, i.e. a rectifier. But a "tunnel diode", according to wikipedia, is not rectifying: In the tunnel diode, ...
2
votes
1answer
359 views

Calculating probability of finding the particle using Dirac notation

An electron can be in one of two potential wells that are so close that it can ‘tunnel’ from one to the other. Its state vector can be written $|ψ\rangle = a|A\rangle + b|B\rangle$, where ...
2
votes
1answer
179 views

Why is quantum tunneling most significant between states of equal energy?

Why is it, that quantum tunneling is only significant between states of nearly equal energy (as claimed here: 'Since tunnelling is significant only between states of nearly equal energy, tunnelling is ...
2
votes
1answer
297 views

What can tunnel through a graphene sheet?

In popularizations, people tunnel through walls or doors. But what can really tunnel through a graphene sheet without tearing it? According to Wikipedia, a single layer of graphene absorbs 2.3 % ...
2
votes
2answers
199 views

Why is there an energy gap in superconductors?

I'm a little out of my depth here... I'm trying to understand quasiparticle tunnelling in superconductor-insulator-superconductor junctions. Many books use the "semiconductor model" to explain this: ...
2
votes
1answer
339 views

In principle, can energy “tunnel” directly out of a black hole? If not, why not?

Energy seems to quantum tunnel through normally impenetrable barriers, so I wonder why not the back side of an event horizon?
2
votes
3answers
438 views

What happens with a tunneling particle when its momentum is imaginary in QM?

In classical mechanics the motion of a particle is bounded if it is trapped in a potential well. In quantum mechanics this is no longer the case and there is a non zero probability of the particle to ...
2
votes
1answer
755 views

What is the derivation of the formula for the probability of transmission through a barrier?

This site has a formula for the transmission probability over a barrier (in transistors): $$ T \propto \exp [-2(2m^*/\hbar ^2)^{1/2}(q\phi)^{1/2} d ]. $$ Where $T$ is the transmission probability ...
2
votes
1answer
2k views

How to solve Schrodinger Equation - Tunnelling

I have to solve analitically the Schrodinger equation in one-dimension with a barrier of potential (tunnel effect): $$ih \frac{d}{dt} U(x,t) = \left[ \left(-\hbar^2 \frac{d^2}{dx^2} \right) + q V(x) ...
2
votes
1answer
57 views

Does quantum tunnelling drill holes in solid state drives?

The solid state drive (SSD) consists of numerous data storage elements. Each element (NAND flash memory element) reminds me of a microscopic battery. An electron is supposed to enter the element ...
2
votes
2answers
207 views

Extra energy in quantum tunneling

In quantum tunneling, the probability of finding an electron inside the potential barrier is non zero . So we can actually find an electron which had an energy $E$ in a place where classically it ...
2
votes
1answer
2k views

How is quantum tunneling possible?

How is quantum tunneling possible? According to quantum mechanics, each particle is represented by a probability density function. This function must be continuous, and therefore when we look at a ...
2
votes
1answer
288 views

Why is Hawking's No Boundary condition described in terms of an instanton if there's no tunneling?

Regarding his take about combining No Boundary proposal with inflation theory (Hawking and Turok), he talks about the "pea instanton". To my very limited understanding I thought instantons were only ...
2
votes
0answers
37 views

Two-Band k.p Model is not Hermitian for imaginary wavevectors

In E. O. Kane's original work on Zener Tunneling, he uses a two-band $k\cdot p$ model for the semiconductor bandstructure: ...
2
votes
0answers
46 views

Tunnelling from a normal metal into a superconductor

a similar question has already been asked in the forum but unfortunately I cannot yet comment and still think that some things left unanswered. My question is in general concerning the tunnelling ...
2
votes
1answer
232 views

Phase Shift of Tunneling Wave

What is the phase shift of a wave that tunnels through a barrier, meaning the difference in phase between the incoming (in front of the barrier) and the outgoing (behind the barrier) waves? For ...
2
votes
0answers
190 views

Definition of a 'tunneling lifetime'

I'm given a one-dimensional potential with two wells, one local minimum at some higher energy and one deep global minimum next to it, separated by a barrier of own shape and height (phase qubit). I ...
2
votes
1answer
191 views

Can someone explain probability flux in the tunneling boundary condition of Vilenkin?

This is what's leading to the notion of a quantum universe tunneling from nothing into existence, right? The idea is that probability flux flows out of superspace (configuration space) at ...
1
vote
3answers
1k views

Why can't light escape from inside event horizon of Black Holes?

The simple answer: Its because Gravity of Black Hole there doesn't allow it. See also this and this Phys.SE posts. Isn't it a classical answer? When we're unable to connect Gravity with Quantum ...
1
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2answers
1k views

From where does a particle get the energy to tunnel?

When a particle is made to confine more and more to a particular position it breaks the energy barrier to get out because of the uncertainty principle. But, from where does the particle get the energy ...
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vote
2answers
626 views

What really happen with resonance inductive coupling

I can't figure out the picture of resonance inductive coupling I can image how magnetic inductive coupling works, It scatter magnetic around one coil and if second coil being near it then induce ...