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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14 views

Number of classical oscillation modes of a Lattice and number of quantum phonons

In solving the Classical model for lattice dynamics [Rossler pag 38] we find that the lattice admits $$d\cdot N\cdot r = \#modes$$ where $d=$dimension of the problem $N=$ number of atoms $r=$ ...
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16 views

What determines a particles probability of creation?

I know when we're discussing events at a quantum level, we deal in probability and not absolutes. What I'm looking to understand, is when articles I've read on particle physics state a particle has a ...
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34 views

How do I calculate momentum for a particle in a box, using the momentum quantum operator?

For a particle in a one dimensional box with $U(x) = 0$ between $x = 0$ and $x = L$ (infinite Potential well) the momentum for $n = 1,2,3,...$ is given by: $$p_n = \frac{nh}{2 L}$$ The wave ...
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1answer
30 views

The GHZ-State in conflict with local realism

Consider three, with respect to their polarisation, entangled particles in the following state: $|\psi\rangle = \frac{1}{\sqrt2}(|H\rangle_1|H\rangle_2|H\rangle_3 + ...
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25 views

Fixing time in Feynman phase space path integral

The phase space version of Feynman's path integral expression for the free particle propagator involves a (formal) sum over paths in phase space with fixed $q$ endpoints and (as far as I'm aware) ...
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3answers
104 views

Why does time evolution operator have the form $U(t) = e^{-itH}$?

Let's denote by $|\psi(t)\rangle$ some wavefunction at time $t$. Then let's define the time evolution operator $U(t_1,t_2)$ through $$ U(t_2,t_1) |\psi(t_1)\rangle = |\psi(t_2)\rangle \tag{1}$$ and ...
2
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1answer
35 views

Why do the two amplitudes need to match together through the region between the boxes?

This is an excerpt from Feynman's lectures 3; Suppose we think of the situation in Fig. 7–3, which has two boxes held at the constant potentials $ϕ_1$ and $ϕ_2$ and a region in between where ...
2
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1answer
38 views

Reflection of an Electron

When a mechanical wave goes from one material to an other, some fraction of it returns back. Same thing with light (massless), but what happens with an electron? When the "wave function" changes ...
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37 views

Do the eigenstates of the Pauli operators correspond to the six directions of the 3D world?

I understand that the six eigenstates of the three Pauli operators $X, Y, Z$ correspond to the six poles of the Bloch sphere. By fixing an orthonormal basis of our physical word, does "measuring Pauli ...
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30 views

Conservation of momentum in Heisenberg's microscope

In working through Heisenberg's microscope, conservation of momentum for the photon and electron tells us that \begin{align} \frac{h}{\lambda}=\frac{h}{\lambda'}\sin\theta+p_x\,, \end{align} where ...
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1answer
35 views

Can something actually be air tight? Sub unit of energy? [on hold]

I thought about space travel and wondered if space crafts are 100% air tight or not. How would we even know if something is air tight or not. There could be a leak that would allow small amounts of ...
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70 views

Quantum Entanglement - How To Interpret [duplicate]

I have thought about quantum entanglement for some time, and I still don't quite understand the reasoning behind the conclusion that entangled particles somehow can communicate their state to each ...
3
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1answer
25 views

One Pion Exchange Potential properties for a two-nucleon system

I'm going through my Nuclear Physics book, and has come across a section called "Properties of OPEP for the two-nucleon system". It start out by considering the n-p system in a singlet spin state ...
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28 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
19 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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44 views

Commutation relation between linear momentum and vector Potential [on hold]

Does the linear momentum and vector potential commute? How can we show their commutation relation ? I am actually trying to find the commutation relation between both linear momentum of an electron ...
2
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1answer
38 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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1answer
23 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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0answers
27 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).
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66 views

Quantum electron and field interactions

What is the proper way to consider the electric field generated by an electron wavefunction governed by the Schrodinger equation? Can you get a result that would match observation, or is this a ...
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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 ...
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1answer
52 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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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 ...
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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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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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167 views

Why is it easier to calculate $\langle \chi|j\rangle\langle j|A| i\rangle\langle i| \phi\rangle$ than $\langle \chi|A|\phi\rangle$?

I was reading Feynman lectures III's Spin One; there at the machinery of quantum mechanics he discusses a situation in which he needs to find the amplitude of finding the particle at ${\chi}$ state ...
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26 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 ...
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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 ...
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54 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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2answers
84 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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59 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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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 ...
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3answers
114 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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1answer
31 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 ...
2
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2answers
93 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.
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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 ...
2
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1answer
49 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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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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38 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
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1answer
60 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, ...
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3answers
105 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 ...
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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 ...
2
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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.
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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?
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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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0answers
46 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 ...
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39 views

which of the many interpretations of Quantum Mechanics most well explained? [closed]

I have been studying the ensemble interpretation by Leslie Ballentine which looks very well explained and has reason for every(almost every) axiom. I am seeking new your opinion.
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27 views

How does Quantum tunneling conserve energy? [duplicate]

How does Quantum tunneling conserve energy? Take a simple example. An electron in hydrogen leaves the single proton it was bound to and escapes without being excited by and interaction. It tunneled ...