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85 views

Why wavefunction becomes exponentially smaller during quantum tunneling?

I am interested in quantum tunneling and I am wondering why the wavefunction of a particle would becomes smaller so that there is a slight possibility of finding it at the other side of a big energy ...
6
votes
3answers
1k views

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 ...
0
votes
1answer
237 views

Meaning of wave function which is in inside of the potential wall? [duplicate]

In particle in square potential barrier problem, we can easily find that some probabilities exist which express how many particles can go beyond of the potential wall. So my question is that, can we ...
1
vote
1answer
386 views

Transmission reflection at step potential mass independent?

I was reading the Wikipedia page about transmission and reflection, and to my surprise, the transmission and reflection coefficients do not depend on the mass of the particle. So in consequence the ...
0
votes
1answer
498 views

Potential step and tunnelling

Imagine a particle with energy $E$ heading towards a potential step with height $V_0$ where $E<V_0$. The particle's wave function is oscillatory before the boundary and exponentially decaying in ...
2
votes
3answers
629 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 ...
0
votes
2answers
2k 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 ...
0
votes
2answers
926 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 ...
7
votes
2answers
807 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?
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) ...