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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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Can a particle be physically observed inside a quantum barrier?

I understand that if a particle approaches a finite potential barrier of height $V_0$ with energy $E < V_0$, there is still a finite probability of finding the particle on the other side of the barrier due to quantum tunneling. My question is, since…
Josh
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In aluminum, how does electricity travel through the surface oxide layer?

Suppose I connect a conductive wire (cross section 1 mm$^2$) to an aluminum object. Since aluminum is highly conductive, electricity will flow smoothly inside the object with little resistance. However, since aluminum is also very reactive, there…
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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 $$ \left( -\frac{\hbar^2}{2m} \frac{d^2}{dx^2} + V(x) \right) \psi(x) = E\ \psi(x), $$ where we assume that…
tparker
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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 its potential energy. and the only difference…
garyp
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How to understand "analytical continuation" in the context of instantons?

Since this is a subtle and interesting question to me. I will give a rather detailed description. I hope you can keep reading it and find it interesting too. For simplicity, in the following I will only discuss the one-dimensional instanton, that…
Wein Eld
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Can our hand pass through a table?

I recently read that "there is a $1$ in $5.2^{61}$ chance that the molecules in your hand and table would miss each other, making your hand go through it". To me, it seems completely false, considering electron repulsion and the high density of…
shrekwes
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Physical intuition for the Wilczek-Parikh tunneling picture of Hawking radiation

There's a naive pop-sci explanation of Hawking radiation, where a particle-antiparticle pair is produced just inside the event horizon. The particle with positive energy tunnels out and escapes, while the one with negative energy falls in, so the…
knzhou
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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 story goes that a virtual particle-antiparticle pair…
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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 enough to adhere to each other in deep space…
Terry Bollinger
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How can quantum tunneling happen conceptually?

I have read in Griffiths' Quantum Mechanics that there is a phenomenon called tunneling, where a particle has some nonzero probability of passing through a potential even if $E < V(x)_{max}$. What I don't understand about this is how to…
Relativisticcucumber
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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 regions to asymptotics of the Airy function solutions…
sferics
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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 rigid impenetrable walls and there is no…
yayu
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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 of $0$ then it can only vibrate between the points…
Joshua
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Why don't electrons tunnel out of atoms?

The overlap of a free electron wavefunction and a bound electron wavefunction is nonzero. So why don't electrons slowly bleed out of atoms? If any wavefunction enters a free particle state it will just escape!
Matt
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What is the kinetic energy of a quantum particle in forbidden region?

I have read that if a particle is trapped in a finite potential well, it has a finite chance to tunnel out from it. Therefore, one can find a particle in a region where its potential energy is greater than its total energy. I was wondering what…
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