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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How did physicist calculate times like $10^{1500}$ and $10^{10^{76}}$ years?

If protons don't decay, iron stars are expected to form via quantum tunneling after $10^{1500}$ years, and they are expected to all have become neutron stars or black holes after $10^{10^{26}}$ to $10^...
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Obtaining Transmission Coefficient of Beam Upon a Linear Potential

I would like to determine the transmission coefficient $\mathcal{T}$ for a particle beam $$\Psi(x,t) = A_o e^{ikx}e^\frac{-iE_ot}{\hbar}$$ with energy $$E = \frac{\hbar^2k^2}{2m}$$ incident upon a ...
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Dirac Delta potential

As we know a particle in attractive Dirac delta potential has discontinuity in the derivative of its wavefunction. I have two questions in this regard: Can a second-order differential equation (the ...
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895 views

Explanation of crystal formation in a Fitzroy's storm glass with the change in weather conditions

I was recently reading about Admiral Robert FitzRoy's storm glass and how it was used to predict the weather conditions based on the formation of camphor crystals in a sealed glass tube containing ...
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Mechanism for collapse of iron stars into black holes via quantum tunnelling

In the wikipedia page "Future of an expanding universe" it refers to the scenario of a future without proton decay. The page talks about how processes would lead to stellar-mass cold spheres of iron, ...
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What does theory say about tunnelling and universe expansion?

Correct me if I'm wrong, my limited understanding of how wave functions work let me assume that they don't "zero out", unless through interferences. I would then imagine that, when a ...
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Tunnelling of alpha particles - explanation

As it is now known because of Gamow, how alpha decay occurs. We have taught this theory in our class in last week. There we have been introduced with a strange phenomenon happening because of which ...
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Why do we say that quantum tunneling is when a particle passes through a barrier they wouldn't classically have enough energy to overcome?

If a particle is in an energy eigenstate, then it must also be in a superposition of both outside the barrier and inside the barrier. So, if we measure the particle to be outside the barrier, I wouldn'...
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If the universe is infinite, would QM allow the existence of "weird" zones? [closed]

If we suppose that the universe is spatially infinite and extends more or less homogenously in all directions without end (having similar galaxies, stars etc.), then we can assume that there is a more ...
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How to convert the problems of quantum mechanics that we usually solve for plane waves to gaussian wavepackets?

I want to solve a barrier potential problem for a Gaussian Wavepacket moving at a velocity v= $\frac{p_0}{m}$. Normally we consider plain wave functions of the following type $$\Psi (x) = Ae^{ikx} + ...
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Question regarding stopping a quantum tunneling simulation and integrating it

There is this wonderful blog that discusses how to simulate quantum tunneling (https://physicspython.wordpress.com/2019/10/27/quantum-tunneling-part-3/) I am new to using python to do physics, and ...
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Single particle tunneling Hamiltonian

In reference to Problem 9, Chapter 2 in Modern Quantum Mechanics by JJ Sakurai, For a single particle tunneling in a 1D double well potential, with position eigenkets $\mid R\rangle$, $\mid L\rangle$....
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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 ...
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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 ...
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Tunneling in Infinite potential well [duplicate]

In quantum mechanical tunneling particle doesn't scale the potential but instead find a short route to cross barrier. Then why is tunneling only possible in case of finite square well potential and ...
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Do two 1D Rectangular Potential Barriers have Bound States?

This question had me thinking about the related 1D problem of two rectangular potential barriers: The potential is zero everywhere but for the two barriers, where it is $V_0$. As ever I am ...
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Why is the conductance of a metal-insulator-metal tunnel junction parabolic?

For bias voltages below the tunnel junction barrier heights (and below the Fowler-Nordheim limit), tunnel junctions have a parabolic conductance as a function of bias. Is this due to the metallic ...
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Transmission Coefficient of Finite Square Well

Now I was calculating the Transmission Coefficients of finite square well potential and found something weird The transmission coefficient is given by $$T=\left[1+\frac{V_o^2\sin^2(2ka)}{4E(E+V_o)}\...
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Is muon-catalyzed fusion a form of pycnonuclear reaction?

Muon-catalyzed fusion is a form of fusion where the electron in a hydrogen atom is replaced by a much heavier muon, which orbits 196 times closer than an electron and allows it to approach other ...
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How unlikely is it that particles tunnel (comparatively) very long distances?

My understanding of quantum tunneling is that when you're not measuring a particle's position you can't know exactly where it is, just where it might be, and that sometimes it happens to be on the ...
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Why do helium balloons deflate?

Helium balloons deflate–even when they are made from metal foil. How does this happen exactly? Is there any chance that quantum tunneling plays a role here? The thought is that the helium atoms inside ...
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How are resistivity and tunneling related?

If we consider a sandwich with three nanometric layers: conductor-insulator-conductor and apply voltage (lower than breakdown voltage) from both sides tunneling will occur. Is tunneling dependent on ...
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Tunneling in Dissipative Environment (II)

This is another question that extends my previous question A Problem on Tunneling in Dissipative Environment. In order to figure my first question out (which I still haven't) I am reading the section ...
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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 ...
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Scanning tunneling microscopy effect (contrast from bottom of 100 Å thick metal layer) analogous to thin-film interference and Newton's rings?

I haven't used a Green's function in 30 years and need some help understanding the use in this context. I. B. Altfeder, D. M. Chen, and K. A. Matveev 1998 Imaging Buried Interfacial Lattices with ...
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Why can't quantum tunnelling carry energy or information faster than light?

A few experimenters have at one time or another claimed that quantum tunnelling allows the transfer of information or energy at superluminal speeds. One was the idea that music was carried across a ...
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Does detecting particle or delayed choice affect quantum tunneling?

As much I have read quantum tunneling is propagation of wave function through barrier, and it is possible because of wave nature of particles. Now my question is will particle tunnel if it is detected ...
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Scattering from finite square well and the transmission coefficient

Suppose we have a typical finite square well where $\lim_{x \to \pm\infty} V(x)=0$ and $V(x)=-V_0$ for all $x\in[-a,a]$ where $V_0>0$. The finite square well admits both bounds state solutions (...
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How does the barrier affects quantum tunneling?

I am picturing a sine wave acting as a barrier for my quantum tunneling experiment, it can be an electric field etc. Now I have an electron whereby a portion of its probability intersects and even ...
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Given Quantum Tunnelling, and a High Enough Velocity, Could Two Objects Theoretically Pass Through One Another?

I apologize if this has been answered before -- The answer may be out there, but I may just not have the proper terminology to find it. I was messing around with Universe Sandbox, and noticed that if ...
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Is tunnel microscope destruct a bit the material, by extracting electrons from the probed material?

The tunnel microscope probes the electrons of a material by quantum tunneling effect. As a consequence of the migration of electrons, is the tunnel microscope "destroying" a bit the material,...
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Why is the alpha particle in alpha decay considered to be in a potential well?

I understand that when modelling alpha decay, it is useful to consider the $\alpha$ particle as being preformed, in a region confined to the daughter nuclei. I also understand that the term $V_{0}$ ...
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Finite Potential Barrier Where $E=V_0$

If we have a free particle of energy E incident on a potential $V$ $$V(x) = \begin{cases}0 & x \leq 0 \\ V_0 & 0 < x < L \\ 0 & x \geq L\end{cases}$$ We find that the wave function $\...
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When an electron tunnels through a barrier, where would it be found when measured? [duplicate]

When an electron with E < V approaches a step in potential energy, the wave function will exponentially decay at the step, meaning there is still a finite possibility of the electron being found at ...
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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 ...
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How does QFT explain QM phenomena?

I've been studying QFT for a couple of years now, and until today I haven't encountered any of the phenomena that I've studied in my QM course: tunneling, entanglement, probability measurements and ...
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What are the differences and similarities between dynamical tunneling and quantum tunneling?

In case of a double well potential, particle can tunnel from one well to another and this process is known as quantum tunneling or tunneling in general. I want to know about dynamical tunneling and ...
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Particle in a classically allowed region vs forbidden region

So what would the momentum be in either of these regions? In terms of the infinite square well where the potential, $V(x) = 0\leq x\leq a$ and infinity otherwise. In the otherwise case, the potential ...
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Quantum Tunnelling Likelihood in Sun

So I have a question in regard to quantum tunnelling. Firstly, I've been given a question to calculate the kinetic energy of a proton inside the sun where the sun has an internal temperature of $$𝑇 ∼ ...
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Can vacuum breakdown occur from a positively charged surface?

Against a sufficiently large voltage, resistance is futile. Although the vacuum is a very good insulator, electrical breakdown can occur even in a perfect vacuum in the presence of a very strong ...
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Energy level splitting in two-state systems

I was learning basic quantum mechanics using Feynman Lectures on Physics. In Chapter 8 Feynman has described ammonia inversion due to tunnelling. Feynman has first used the base states as the two ...
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Energy Levels in Double Finite Well potentials [closed]

Why is there a behaviour where $E_1$ and $E_2$ are close to each other? This question is already answered before but I did not understand the explanation about symmetric and asymmetric terms as I do ...
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Energy levels splitting in double-well potentials

As it is well known, the tunnel splitting (which are certain differences between energy levels) is the characteristic of the energy spectrum for the double-well potentials. When we calculate the ...
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Materials based on quantum tunneling: conductivity

Suppose you have a nanocomposite wire in which electrons can move through it exclusively with the electron tunneling between conductive nanoparticles that are within optimal distance (like in figure ...
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Why do helium fuse in the Sun?

Initially there are lots of hydrogen atoms and trace elements in the Sun. Despite insufficient energy for the hydrogen to fuse in the core, quantum tunneling saved the day and invoke proton-proton ...
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What is the significance of the electron's wavelength for Momentum and Energy Resolved Tunneling Spectroscopy (MERTS)?

The technique called momentum and energy resolved tunneling spectroscopy (MERTS) is based on quantum tunnelling, whereby an electron can traverse a barrier which has a thickness of less than 3nm, by ...
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What actually is a potential barrier in quantum mechanics?

I'm new to quantum mechanics, and I was wondering what actually is a potential barrier in quantum mechanics? I understand that it is similar in a way to a hill in classical mechanics except that we ...
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How does the energy splitting in a double well potential scale?

It is well known in quantum mechanics that in an 1D double well potential there is an energy splitting between the ground state $\psi_0(x)$ and the first state $\psi_1(x)$ despite them being nearly ...
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Possibility of staying within nucleus for a electron according to Uncertainty Principle

Academic Problem: According to Uncertainty Principle, show that electron can't stay within nucleus. That's a general problem indeed. Anyway, we know that uncertainty of position in this case can't ...
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The integrals in the paper (Hawking radiation as tunneling)

In the paper PRL 85(2000), 5042, "Hawking radiation as tunneling", by Parikh and Wilczek, https://arxiv.org/abs/hep-th/9907001, there are some integrals, such as Eqs.(6) and (8). They are ...

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