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
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5answers
212 views

How is anything *not* ultimately a position measurement?

Consider measuring the momentum of an electron. You pass it through some kind of electromagnetic field, it strikes a photodetector (e.g. a CCD), and you back-calculate out the momentum of the ...
2
votes
3answers
146 views

What is the physical intuition behind the fact that 'energy is not continuous'?

First of all I am a novice regarding my knowledge of quantum mechanics. But curiously I do want to know what is the problem if energy is continuous like spontaneously flowing tap water. In fact I ...
4
votes
0answers
67 views

References to Mechanics (Classical, Quantum, Statistical) using Time-Scale calculus?

Time-Scale Calculus, is a theory which unifies ordinary (plus fractional and q-) calculus with discrete (and finite differences) calculus. In a sense, in a similar way the Lebesgue integral (or ...
0
votes
2answers
71 views

Indistinguishable particles and probability density

I am given the following (probably simple) exercise, but I think I misunderstand something: Let $\psi_{a,b}(r_1,r_2)$ be a two-particle state, calculate the probability density for distinguishable ...
3
votes
3answers
515 views

Wavefunction, probability and impossible events

A friend of mine asked me a question, which I considered trivial at first, but after a while gave rise to some doubts. For instance, we have a potential well in 1 dimension defined by $$ V(x)= ...
-1
votes
0answers
51 views

How can we prove the commutator $[F(a^{\dagger}a),a^{\dagger}a]=0$

The spin operators defined by the Holstein-Primakoff transformation are $$ S^{+}=\hbar \sqrt{2S}a^{\dagger}\sqrt{1-\frac{a^{\dagger}a}{2S}} \\\ S^{-}=\hbar \sqrt{2S}\sqrt{1-\frac{a^{\dagger}a}{2S}}a ...
0
votes
0answers
23 views

Electron transmission in Landauer formalism: why just imaginary part?

In Landauer formalism the electron transmission function is defined as $T = Tr(G_M^\dagger\Gamma_LG_M\Gamma_R)$ where $G$ are Green's function of subsystems, index $L$ and $R$ means subsystem of ...
0
votes
1answer
29 views

Why is the unitary matrix relating the gamma matrices and their complex conjugates antisymmetical?

In Messiah's Quantum Mechanics Vol. II, properties of the Dirac matrices are derived. There is so-called fundamental theorem, which states that, Let $\gamma^\mu$ and $\gamma^{'\mu}$ be two systems of ...
1
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3answers
97 views

Can excited electrons fall back to their ground state without the emission of photons?

In gas discharge lamps, for example, a current composed of ionized atoms excites the electrons of the atoms of the gas, and when they fall back to their ground state photons are emitted. Why is the ...
4
votes
2answers
254 views

Do the probability density and the probability current density have a unit

I could not find what is the probability density and the probability current density of one-dimensional Schrödinger equation units?
3
votes
1answer
43 views

Is there a lower bound on energy needed to transfer one bit of information?

Let's say we want to transmit information between to stations (points in space). Is there a minimal energy required to transfer a single bit of information, assuming that we tolerate that the bit ...
4
votes
2answers
61 views

Partition function containing QM?

I am wondering about the partition function of the classical microcanonical ensemble. It contains Planck's constant and also an indistinguishability argument about the particles I am looking at and I ...
1
vote
1answer
55 views

What do position and momentum representations represent in QM?

In QFT we classify field operators according to how they transform under a given symmetry, i.e. in their being a basis for some representation of the symmetry group of the Hamiltonian/Lagrangian. This ...
1
vote
2answers
92 views

Do electrons “check in” at the quantized energy radius before they leap?

Quantum jumps inside atoms always have the same energy, at least in a hydrogen atom when jumping from $n=1$ to $n=2$, like from a 1s1 to a 2s1 state. My question is, if an electron can be anywhere in ...
-1
votes
0answers
17 views

Quantum camera using euclidean rotation and kabbalah

I've been playing around with procedurally generated images and the kabbalah/tesseract the last few weeks. Imagine a 3D cube sitting on top of a 2D colour wheel. One thing I noticed is that 3D ...
0
votes
2answers
51 views

Expectation value expression Quantum Mechanics

Whilst working on a project I kept stumbeling across two different expressions for the standard deviation $\Delta{X}^2 = <(X - <X>)^2 >$ and the other $\Delta{X}^2 = <X^2> - ...
1
vote
2answers
46 views

How does EM heating cause motion?

Similar to how does heating cause motion, I'm trying to understand how a photon imparts motion to an atom, i.e. adds heat to a gas. I'm going to hazard a guess, and suggest this occurs something ...
1
vote
2answers
74 views

Energy-Time Uncertainty Principle and Photons

Heisenberg's uncertainty principle states that: $$ \Delta E \cdot \Delta t \ge \frac{\hbar}{2} $$ It is clear that this has nothing to do with the accuracy of our measurements, but rather is a ...
1
vote
3answers
114 views

Schrödinger equation derivation and Diffusion equation

I am aware of the debate on whether Schrödinger equation was derived or motivated. However, I have not seen this one that I describe below. Wonder if it could be relevant. If not historically but for ...
2
votes
1answer
114 views

What obstacles does de Broglie's pilot theory have to overcome? [duplicate]

I have been reading through a Wired article on pilot wave theory which talks about new evidence in support of Louis de Broglie's concept of pilot theory through experiments showing that the droplet in ...
4
votes
4answers
189 views

How big is an excited hydrogen atom?

Suppose an empty universe with the exception of a single hydrogen atom (1 proton, 1 electron). The electron may be in its ground state or it may be excited a certain number of levels. Suppose it is at ...
3
votes
1answer
141 views

Susy QM and Atiyah-Singer index theorem

Consider maps $t\mapsto x^i(t)$ from circle to some Riemannian (spin) manifold and lagrangian $$ \mathcal L = \frac12 g_{ij}(x) \partial_t x^i \partial_t x^j + \frac12 g_{ij} \psi^j \left(\delta^i_k ...
5
votes
2answers
90 views

How exactly does applying the Equipartition Theorem to radiation leads to UV catastrophe?

I'm reading a book by George Gamow, "Thirty years that shook Physics" and have trouble understanding his way of describing the UV catastrophe. In a first part he points out that applying the ...
1
vote
1answer
74 views

Difficulties in understanding basic energy equation in quantum mechanics [duplicate]

While reading a text book about basics of Quantum Mechanics, I came across a situation in which it is said that $E=\hbar\omega$ and also $E = \frac12mv^2=p^2/2m$ where $h$ Planck's constant ...
2
votes
0answers
55 views

Statistics of many body systems in pure states

My understanding of describing a system in thermal equilibrium is that we introduce an ideal thermal reservoir for convenience and then imagine that the system+reservoir samples all states of constant ...
1
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0answers
21 views

Fluctuation-dissipation in a quantum Ising Model

For the classical Ising model, the fluctuation-dissipation theorem tells us that the Magnetic susceptibility is proportional to the variance of the magnetization. Is there an equivalent relation for ...
0
votes
1answer
16 views

post selection and instantaneous communication [duplicate]

Does post selection lead to instantaneous communication between two points in space? Below is the scenario: Take two entangled qubits A and B. Seperate them out in space. Post select on qubit A to be ...
2
votes
0answers
79 views

Symmetry, gauge, and projective symmetry group (PSG)?

My following questions come from the understanding of the relations between the PSGs for two gauge-equivalent mean-field (MF) Hamiltonians (or MF ansatz). Considering the Schwinger-fermion ...
0
votes
2answers
56 views

If we were to hold a single atom in our hand, would it feel solid? [closed]

If we were to hold a single atom in our hand, would it feel solid? In addition, do all the matter that we feel solid actually a wave of probability? I'm not a physicist anyway.
2
votes
0answers
38 views

Tunneling from Dirac material into Schrodinger material?

When a Dirac material, like graphene or TI, has a connection with a normal metal which Schrodinger equation govern on their carriers, how could we manipulate the tunneling of electron from Dirac side ...
0
votes
1answer
55 views

What is the time dependent expectation value for momentum

For an electron in an equal linear superposition of two eigenstates in a one-dimensional infinitely deep square potential well of width L, how do you isolate the time dependent part of the expectation ...
0
votes
1answer
60 views

Working towards finding Clebsch-Gordan coefficients for a single electron

I'm really confused about a problem involving a single electron which eventually wants me to calculate Clebsch-Gordan coefficients. I think this is probably because, I've only ever seen examples done ...
1
vote
0answers
25 views

Why isn't there a different phase after fourier transformation in two lattices

I am trying to understand some solutions for graphenes energy dispersion. While most of it is clear, I don't get one step, when changing into k-space. Consindering two sublattices A and B with ...
0
votes
0answers
20 views

Screened potential of charged impurity in a 2-dimentional electron gas

What's the analytical relation of screened potential of charged impurity in a 2-dimentional electron gas?
2
votes
1answer
60 views

Unitarity and measurement

I used to believed that the wavefunction collapse came from the interaction of the system we want to measure {S} with the measurement apparatus {M} : {S} undergoing a non unitary transformation, but ...
3
votes
2answers
81 views

Confusion with rotation operator definition in Shankar

In Shankar quantum mechanics on page 306-307 it has the following: 12.2. Rotations in Two Dimensions Classically, the effect of a rotation $\phi_0\mathbf{k}$, i.e., by an angle $\phi_0$ about ...
8
votes
3answers
391 views

What do the Pauli matrices mean?

All the introductions I've found to Pauli matrices so far simply state them and then start using them. Accompanying descriptions of their meaning seem frustratingly incomplete; I, at least, can't ...
1
vote
3answers
148 views

How do we physically apply the operators of quantum mechanics on a particle?

What do we have to perform physically that is equivalent to applying those quantum mechanical operators on a state $|\psi\rangle$? Edit: I have removed the part I was asking regarding measurement ...
0
votes
0answers
22 views

Quantum Forbidden Regions-Band Theory

In systems where certain regions are classically forbidden for a particle, quantum mechanics permits a finite probability of finding the particle in those regions. However, in band theory of metals, ...
0
votes
3answers
88 views

Repeating a measurement vs uncertainty

The wikipedia says on measurement in quantum mechanics that: Repeating the same measurement without any evolution of the quantum state will lead to the same result. On the other hand, doesn't ...
4
votes
1answer
110 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 ...
7
votes
2answers
245 views

Renormalization in non-relativistic quantum mechanics

I read many articles about renormalization in the Internet, but as I currently don't know much of QFT (currently just studying classical field theory and QM), and as all this looks quite interesting, ...
-1
votes
0answers
28 views

Quantum Liouville condition?

I understand there is the quantum-Liouville equation, namely the Von-Neumann equation, but does Liouville's theorem apply to the Wigner distribution too? What about the Moyal bracket, is that a ...
2
votes
2answers
80 views

Picturing electrons

I used to think that the electron is a particle orbiting the nucleus, but now I know that the electron can be also thought of as a standing wave. That's kind of like saying that a curve is both ...
2
votes
2answers
76 views

Unitary change of X Basis: Shankar Exercise 7.4.9 [closed]

I'm currently working through Shankar's Quantum Mechanics and am stuck on one of his exercises. In Exercise 7.4.9 Shankar would like us to show that: if $\mid x \rangle$ is changed to $\mid ...
2
votes
0answers
24 views

Meaning of Wigner Function In a Single Variable

We know that if we integrate the Wigner function $W(x,p)$ against one of the variables, we get the marginal probability distribution. But how should we interpret say $W(x)$, i.e. its projection into ...
1
vote
0answers
208 views

Do these photographs depict the Higgs Field?

[PHOTO 1] Colter Dallman wrote in his paper - Space, Density, Relativity and Higgs Field Occupancy - (available online): ...
2
votes
0answers
91 views

Para and ortho hydrogen angular momentum values

In Wikipedia, it is said that: Orthohydrogen, with symmetric nuclear spin functions, can only have rotational wavefunctions that are antisymmetric with respect to permutation of the two protons. ...
1
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0answers
24 views

Solving of one dimensional potential sets [closed]

is a set of 1D potentials which i need more examples and their solutions containing transmitting states, bounded states, scattering states and coefficients. I searched with 1D potential ...
0
votes
2answers
73 views

Quantised Angular Momentum?

So when learning about the Bohr model of hydrogen and de Broglie waves, it was shown that treating the electron of hydrogen as a de Broglie wave results in the relationship $$L=n\hbar$$ However, when ...