Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy and the uncertainty principle and is generally used in single body systems. Use the ...

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240 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 ...
2
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1answer
20 views

variation of electrostatic potential on moving radially outwards from the nucleus of an atom

I was wondering how would the electrostatic potential change on moving radially outwards from the nucleus in an atom, considering the effect of the electron clouds around it.
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2answers
89 views

Why can the probability function for a particle in an infinite square well be larger than 1?

For a particle in a one dimensional infinite potential well of width $L$ the probability function is: $$P_n(x)=\left(\frac{2}{L}\right)\sin^2\left(\frac{n\pi x}{L}\right)$$ for $0\leq x\leq L$. The ...
2
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1answer
41 views

Diagonal part of the configuration space of two indistinguishable quantum particles

Why is the configuration space of two indistinguishable particles given by $\frac{M^n-\Delta}{S_n}$? My question is about the $\Delta$. (Notation: $M$ is the configuration space of 1 particle. $M^n$ ...
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2answers
322 views

Geometric quantization of identical particles

Background: It is well known that the quantum mechanics of $n$ identical particles living on $\mathbb{R}^3$ can be obtained from the geometric quantization of the cotangent bundle of the manifold ...
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0answers
30 views

Liouville's theorem in quantum mechanics

Is there any theorem in quantum mechanics which relates conservation of any physical quantity (say density) just like Liouville's theorem does in classical mechanics?
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1answer
25 views

Bragg's interference

This may be a little of a stupid question. But I was looking at a diagram describing Bragg's Law of Diffraction. and I was like...how can an interference happen if wave beam C and wave beam C' are ...
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2answers
86 views

$[A_1, H] =[A_2, H] = 0$ but $[A_1, A_2] \neq 0$?

I am having a difficult time understanding this problem. Suppose $[A_1, A_2] \ne 0,$ $[A_1, H] = 0,$ $[A_2, H] = 0.$ Show that the energy eigenstates of $H$ are in general ...
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0answers
28 views

What is the explicit decay width formula for a four body decay?

I'm trying to calculate the decay width for a theory with one particle having a decay mode into 4 particles. Does anyone know the explicit formula for this (not the generalized decay formula).
3
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1answer
281 views

Least Action Principle (Classical and Quantum Theory)

I) My first question would be "why should classical systems obey the principle of least action ?" When we find out the propagator in quantum physics, we find the amplitude to be equal to the sum over ...
1
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3answers
232 views

Electron as a standing wave and its stability

1. When it was an era of classical mechanics we used to believe in the Bohr's atomic model. It interpreted electrons as particles (although I couldn't understand how come Bohr who interpreted ...
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1answer
34 views

Probability density function as number of particles per unit volume?

In this book Quantum Mechanics by P.J.E. Peebles pg 365 it hints at the idea of the wave function been the probability of finding $n$ particles per unit volume. I have looked in other books and on ...
0
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1answer
55 views

Can the uncertainty principle be redefined for different standard deviations?

$$\sigma_x \cdot \sigma_p \ge {{\hbar} \over {2}}$$ Where the $\sigma$ is the standard deviation. What happens to the inequality if you use a different definition of $\sigma$. For instance what ...
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0answers
17 views

What makes electrons behave like particles or waves at different times? [duplicate]

I am quite puzzled about the theory that electrons or light often behave as particles and sometimes as waves. So, I wanted to know more about this phenomena and what happens when and why.
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1answer
39 views

Is harmonic oscillator continuous variable system?

In the literature I have seen that the notions "our system is continuous variable system", "Hilbert space of our system is infinite" were used as if they were equivalent. For example for harmonic ...
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0answers
12 views

Spin-orbit coupling of low band gap vs large band gap semiconductors

Why do low band gap material III-V semiconductors, like InAs, show a spin orbit coupling effect higher than large band gap semiconductors? Please give me some references if possible.
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0answers
27 views

What causes the Shubnikov-de Haas Oscillations?

If I have a 2DEG with a voltage in the $x$-direction and a $B$-Field in the $z$-direction (so I also get a hall-voltage in the $y$-direction (classicaly)). But if I do this stuff at low temperatures I ...
2
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1answer
119 views

Quantum fluctuation

According to the quantum fluctuation concept, a particle and its corresponding antiparticle appear out of nothing only to annihilate and emit some energy in the form of electromagnetic waves. Does ...
13
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1answer
474 views

How to evaluate this sum of coupling coefficients?

I would like to evaluate the following summation of Clebsch-Gordan and Wigner 6-j symbols in closed form: $$\sum_{l,m} C_{l_2,m_2,l_1,m_1}^{l,m} C_{\lambda_2,\mu_2,\lambda_1,\mu_1}^{l,m} \left\{ ...
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1answer
29 views

Delayed choice measurement subsequent analysis

This is a variant associated with the Scully and Druhl signal-idler photon delayed choice experiment, as described and discussed in Brian Greene's Fabric of the Cosmos. The commentary notes the ...
2
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1answer
96 views

Why electron can not be found at some node locations in the infinite potential well?

Consider electron in an infinite potential well, studied in quantum mechanics. Position probability density of the electron is $$ P_n(x)=\left(\frac{2}{L}\right)\sin^2\left(\frac{n\pi x}{L}\right)$$ ...
3
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0answers
55 views

Is there a quantum mechanical analog to classical rheonomic constraints wherein the Hamiltonian is not the total energy?

The Wikipedia article on the Hamiltonian operator in QM says that the Hamiltonian corresponds to the total energy of the system, but qualifies that statement with a "in most cases" tacked on the end. ...
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1answer
33 views

Resistance of a cloud of free electron gas by Kubo formula?

How much is the resistance of a cloud of free electron gas, if at all? How much is the resistance of a cloud of free electrons in a periodic potential? Did anyone calculate it using the Kubo ...
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0answers
35 views

Approximate Electric Potential $V$ so that it is of the form $V(r) + V(\phi) + V(z)$

I'm trying to simulate the conductivity of a nanowire that is modeled by a cylindrical shell of infinite potential with benzene rings in the core of the wire. (This is based on a coiled-coil protein ...
0
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3answers
410 views

Double slit experiment observation

In the double-slit experiment, if you shoot particles through the slits one by one and observe which slit they travel through, is there still an interference pattern on the screen behind the slits? If ...
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2answers
60 views

Physical Meaning of Phase Ambiguity

What is the physical significance of multiplying a quantum state $|A>$ by a phase factor $e^{i\theta}$. This does not have any effect on the normalization of the state so what is it physically? ...
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3answers
119 views

Is Hamiltonian a differential operator in second quantization?

Normally, a free particle Hamiltonian is written $$ \hat{H} = - \frac{\hbar^2}{2m} \Delta $$ which is a differential operator because Laplacian $\Delta$ is. On the other hand, in second ...
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0answers
19 views

Photons absobtion during quantum jump

According to this article a quantum jump CAUSES photons absoptions. Does it mean that if there is no photon around quantum jump is impossible? https://en.wikipedia.org/wiki/Atomic_electron_transition ...
2
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2answers
95 views

Do atoms behave like waves? [duplicate]

I've heard someone state that the double slit experiment can also be done with atoms, not just electrons or photons of light.
4
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1answer
207 views

Good source for numerical simulations of Wigner function?

I'm interested in simulating the time evolution of a Wigner function for a harmonic oscillator (and possibly some other potentials) and I can't seem to find a good resource for that. My background in ...
2
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1answer
1k views

Weak measurement and Hardy's paradox

How the notion of weak measurement resolves Hardy's paradox?
2
votes
2answers
152 views

What aspect of quantum mechanics forces probabilities to be (conventionally, at least) central?

I understand how to compute probability distributions and expected values and such from quantum states, but a lot of treatments of QM make it look like this is what the wavefunction is essentially ...
0
votes
1answer
131 views

Slit width for minimum spot size in electron slit diffraction if involving uncertainity principle

I don't believe the following is an accurate description of the physical but a homework problem to help understanding. A beam of electron of energy 0.025 eV moving along x-direction, passes ...
1
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1answer
44 views

Relativistic probability amplitude of a particle to be in certain position

In the book “The story of spin” by Tomonaga on page 110, it says They insisted that a concept like "the probability of a particle to be at $x$ in space" is meaningless for relativistic ...
2
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0answers
100 views

Can the Born rule be derived? [duplicate]

$\renewcommand{ket}[1]{|#1\rangle}$ If we have a particle and we know the initial state $|\psi\rangle$ of everything that is relevant, and we know the full Hamiltonian $H$, then we should be able to ...
0
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0answers
48 views

Does Only Flat universe have zero energy? [closed]

Hello I am very new to cosmology and quantum physics. I need some basic understanding (in LAYMANs term )of the following: I read that only closed universe has zero energy. But I heard Astrophysicist ...
11
votes
2answers
531 views

Are Thomas Breuer's subjective decoherence and Scott Aaronson's freebits with Knightian freedom the same things in essence?

In his remarkable works (1,2 and their recent development 3) Thomas Breuer proves by diagonalization the phenomenon that the observer cannot distinguish all phase space states of a system where he is ...
2
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1answer
50 views

What is the physical significance of Compton wavelength?

Wikipedia says, The Compton wavelength represents the quantum response of mass to local geometry. What does it actually mean?
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1answer
102 views

Path dependent phase in quantum mechanics

In elementary treatments of quantum mechanics, we are taught that the wavefunction of a single particle is complex valued ($\Psi : \mathbb{R}^3 \to \mathbb{C}$). In particular, the wavefunction has a ...
0
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1answer
41 views

Can we extract positrons from gamma rays?

If gamma rays undergo pair production is there a way to say, deflect and collect the positrons using magnetic fields?
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1answer
69 views

Question about Planck's constant

How did Dirac or whoever came up with it know that the momentum operator in quantum mechanics is $-i\hbar\frac{d}{dx}$? How did he know the $\hbar$ was in there? How did all these physicists know ...
2
votes
1answer
62 views

Basis states for many-particle system

I'm reading these notes about second quantization. In section 1.4 the author introduces many-particle wavefunctions. But I can't understand how basis are defined here. I know that if $\{\chi_i | i=1, ...
0
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1answer
48 views

Light changes wavelength in the presence of gravity, can the quantum theory of gravity explain this?

If light changes wavelength in the presence of a gravitational field, how can this be described by the quantum theory of gravity?
0
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1answer
22 views

Semi-infinite / Asymmetric potential well

I'm asked to come up with an ansatz and solve for the coefficients of a asymmetric infinite potential well, where: $$ V = \begin{cases} \infty \text{ for } x< 0 \\ V_0 \text{ for } 0 \leq x \leq L ...
15
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4answers
203 views

Information Retrieval

This question is motivated by the issue of information retrieval from black holes, but it is essentially a question about quantum information. It is widely believed (in certain circles) that the ...
1
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3answers
107 views

Wave Function concept

What do we mean when we say wave function of electron? Does it mean wave nature of electrons? I am really confused.Without clearing this confusion i cannot proceed to molecular orbital theory.I am ...
0
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3answers
271 views

Quantum Mechanics in Electric Field

I am working on a problem which looks like this. Consider a charged particle with charge $q$ trapped in a box of length $L$ with finite constant potential $ V_0 $ on both ends. A constant (static) ...
2
votes
2answers
24 views

What happens to a radioactive element or isotope's electrons when it undergoes alpha decay? [duplicate]

It seems to make sense that when an atom loses two protons, it would lose two electrons as well, but I don't actually know what happens.
0
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1answer
31 views

Circular polarisation destroying interference pattern for double slit

I have been trying to mathematically explain the empirical result that putting orthogonal polarisers (quarter-wave plates) behind the two slits of a double-slit setup will erase the interference ...
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1answer
94 views

What is the classical counterpart of an eigenstate?

Does this question make sense for every system or just some? If it makes sense, it is a periodic orbit?