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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 ...
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63 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 ...
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Is energy lost in an elastic tunneling process?

Suppose we had two metal plates separated by an Angstrom. Now, apply a voltage $V$ between the two metal plates. There will be a tunneling current $I$ between the metal plates. Since $P=IV$, does ...
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77 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 ...
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137 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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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 ...
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47 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 $E$ ...
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63 views

Quantum tunneling in a time dependent potential

I wonder if I could use the technique for finding the tunneling rate given by $$ \Gamma=2 \mbox{Im} F$$ where $F$ is the free energy in case of time dependent potentials? Relevant to the previous ...
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2answers
156 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 $c$. ...
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1answer
263 views

Tunnelling through a Dirac potential barrier

I am reading a QM book by Griffiths, which says it is possible for wave particle to tunnel through a barrier formulated by a Dirac function. This function is known to peak at infinity and also ...
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256 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 ...
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511 views

Quantum mechanics potential barrier problem [duplicate]

While reviewing some quantum mechanics, I cam across a very interesting situation. For a potential barrier, if a particle has an energy $E$ less than the potential barrier $V_0$, it is possible to ...
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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 ...
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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 ...
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168 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 ...
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2answers
213 views

Quantum tunneling and a football permeating a wall

I was wondering if I can say to a layman that "upon throwing the ball on a wall an enormously large number of times, there is a small probability that the ball will go through the wall", while ...
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2answers
382 views

Quantum tunneling is faster than light travel?

Quantum tunneling is faster than light travel ? My reasoning is that the particle cannot be detected inside the tunnel so if it travels from A to B it must be instantly going from A to B , hence ...
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968 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 ...
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516 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 ...
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403 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 ...
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1answer
183 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 ...
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187 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 ...
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216 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?
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Could Dark Matter be a manifestation of tachyons tunnelling between black holes?

Among the many Dark Matter candidates, I wondered if there are any along the lines of the title. The inner horizon of a black hole, with its mass inflation, and/or the high spacetime curvature, seems ...
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312 views

Where does the “borrowed energy” come from in Alpha decay?

I was also thinking about the uncertainty principle in regards with energy & time. The question of something like: Alpha tunneling out of the nucleus is where this can be invoked, but having an ...
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3answers
266 views

Why is the tunnel effect of solid matter not observable in macroscopic objects?

Assume I place a tea cup on a table (say, about a centimetre thick). Quantum mechanics tells us that the wave function for the nuclei and electrons of the cup is not zero below the table (while being ...
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Euclidean quantum gravity and gravitational instantons

I have some questions concerning the calculations made by Hawking in the 80-90's using Euclidean (canonical) quantum gravity on gravitational instantons. Were those tunnelings only between identical ...
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3answers
127 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 % ...
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196 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 ...
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1answer
154 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 ...
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1answer
1k 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) ...
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326 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 ...
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2k 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. ...
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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. ...
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503 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 ...
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769 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 ...