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 quantum-field-...

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π , σ - atomic transitions with respect to a quantization axis

In the absence of a magnetic field, how does one physically (i.e perhaps in a thought expt) access delta_m = 0 or +-1 transitions since (as I understand it) the choice of quantization axis is ...
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1answer
38 views

What happen if adiabatic evolution fails?

Adiabatic theorem states that: A physical system remains in its instantaneous eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalue and the rest ...
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1answer
113 views

Why are general wave functions expressed in terms of energy eigenfunctions?

I have read that the eigenfunctions of any hermitian operator can be used as a basis to express any function, but I have only ever really seen the eigenfunctions of the Hamiltonian used. Why is this? ...
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0answers
50 views

Why isn't there a Time Operator in Quantum Mechanics? [duplicate]

I was wondering about a scenario where you subject a quantum particle to an intense gravitation field. Why can't we apply a sort of time operator to the particle to see how time changes for the ...
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3answers
46 views

Mean energy of free electrons

My textbook states that the mean energy of free electrons within a solid state is given by $$ E_{av} = \frac{U}{N} = \frac{\int_0^{k_f}D(k)E(k)dk}{\int_0^{k_f}D(k)dk} $$ where $D(k)$ is the density of ...
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56 views

non-negative energies

Can someone help me with the following question: given the hamiltonian: $H=\frac{1}{2m}(iP-\hbar f(X))(-iP-\hbar f(X))$ where $f(x)$ an analytic real function. prove that the ...
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47 views

How to construct Hermitian(quantum) operator from a physical experiment?

Suppose I want to study a quantum mechanical quantity of a single particle. I have designed an appropriate apparatus, accuracy of which is limited by relevant laws of quantum theory. I have obtained a ...
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3answers
71 views

de Broglie's relation derivation

While going through de Broglie's relation in my textbook I was stuck by a derivation: Here $$\ E=mc^2 $$ has been applied to photons. That confused me as I thought that mass of photon=0 but a ...
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25 views

Why does the nuclear force become stronger with distance? [duplicate]

Also how factual is the explanation? Is it mostly philosophical like say Many World's 'theory' or is the explanation pretty straight forward with little to no dispute?
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3answers
319 views

Does the entanglement depend on the basis?

Let's say, we have a composite system $A\otimes B$. We take the basis for $A$ as $|i\rangle,|j\rangle...,$ the basis for $B$ as $|\alpha\rangle,|\beta\rangle....$ Then an entangled state is a state ...
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2answers
68 views

In handling two 1/2-spin particles, why is there only one singlet state? [closed]

Why is $\left|\uparrow\uparrow\right\rangle +\left|\downarrow\downarrow\right\rangle$ not discussed, despite having a total spin s = 0?
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1answer
18 views

Oscillator in Energy Basis Lowering and Raising Operators

On page 205 of Shankar's Intro to Quantum Mechanics, equation 7.4.12 does not make sense to me. I understand why a|e> is an eigenvector and why e-1 is its Eigenvalue, but I don't understand how that ...
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1answer
22 views

Two Slit Experiment with polarized filters

If I did a two slit experiment with linear polarized filters in the two paths presumably I would see not interference if they were a 90 deg to each other. If they were aligned presumably the ...
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0answers
24 views

What is the significance of the assumption of “full energetic degeneracy” in this paper?

I'm reading the new paper "Foundations of statistical mechanics from symmetries of entanglement" (available on arxiv), in which the authors Deffner and Zurek note that the quantum microcanonical state ...
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2answers
59 views

How do Rabi oscillations act on the relative phase of state kets

Suppose we have a system with a lower state $\left|{\downarrow}\right\rangle$ and and upper state $\left|{\uparrow}\right\rangle$, coupled by a pulsed electromagnetic field. I thought that from an ...
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1answer
21 views

Scattering from a step potential barrier

Suppose a potential barrier of the form $$ V(x) = \begin{cases} V_0 & x>0 \\ 0 & x<0 \end{cases} $$ Then, for energy $E$ such that $E < V_0$, we have that the transmission and ...
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1answer
56 views

How did physicists conclude that 98% of mass is due to the strong force?

On a video on YouTube called 'weak and strong nuclear force (9/15)' at 0:55 a scientist said that 98% of mass is due to the strong force.
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0answers
47 views

Hamiltonian formulation of the semiclassical Model of electrons

I'm currently reading the book Solid State Physics by Neil W. Ashcroft and N. David Mermin. In Chapter 12 they introduce the "Semiclassical Model of Electron Dynamics". In short: After having solved ...
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25 views

Why is the phase change of a reflected light ray one quarter wavelength?

Suppose a photon beam impinges on a half-silvered plate such that half of the photons are reflected and other half are transmitted. If $\lvert A\rangle$ is the state vector of the incident ray, and $\...
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0answers
65 views

Definition of a gapless spin liquid

I understand the definition of a gapped spin liquid: it's a gapped, topologically ordered spin state - i.e. there does not exist a local unitary transformation that takes it to a product state in ...
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1answer
155 views

Can photons move in parallel?

Is it possible that two photons move in parallel, on the same trajectory - having the same wavelength, but differ in phase? Is it fundamentally possible on the level of quantum mechanics? Is it ...
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2answers
54 views

Uncertainty principle-Exact Measurement of one observable possible?

I'm currently learning for my exam in physical chemistry and have the following question: According to the uncertainty principle the momentum and the location cannot be measured exactly at the same ...
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39 views

Would it be possible to foresee the quantum theory via this thought experiment?

If the Newtonian understanding of universe (I only mean the philosophical understanding, not the scientific theory) would be correct, then we could build a machine that can observe the solar system ...
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26 views

Distinguishing Insulator, Metal, Superconductor by a flux insertion argument

I have the following argument to distinguish Insulator, Metal and Superconductor. For simplicity let's consider electrons on a circle and thread one quantum of flux (e$\Phi_0 = 2\pi$) through it (or ...
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1answer
55 views

How to prove that quantum computers can't solve problems outside PSPACE quickly?

What are general methods to prove that certain complexity class is not proper superset of PSPACE class, and how to apply them in quantum case (for BQP class, for example).
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5answers
215 views

Schrödinger's cat being “both dead and alive”

Famously, Schrödinger's cat is found to be both dead and alive within a closed system - at the mercy of quantum mechanics. But why is the cat "both dead and alive"? For the Copenhagen interpretation, ...
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0answers
40 views

What are the differences (if any) between the Dyson's series definition and the “in/out” definition of the $S$-matrix

So long, in my QFT courses, I've seen two definitions of the $S$-matrix: The first, more elementary, definition is given in the interaction picture: $$S=\text T \lbrace \exp [-i\intop \text d ^4 x \,...
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3answers
147 views

No-Cloning and Uncertainty: Connections or Misconception

In chapter 9 of Scott Aaronson's book "Quantum Computing Since Democritus", he make interesting but peculiar claims relating the no-cloning theorem and the Heisenberg Uncertainty Principle (HUP). Here ...
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0answers
27 views

Anharmonic quantum oscillator with momentum perturbation

Given the following quantum oscillator for a particle with mass $m$, and perturbation $-\gamma P$ ($\gamma$ is a constant): $$H=\frac{P^2}{2m}+\frac{1}{2}m\omega^2X^2-\gamma P$$ One could find the ...
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2answers
58 views

How do I get observables to calculate uncertainty?

Given an infinite potential square well with $0<x<L$, I need to calculate the uncertainties of position and momentum. The eigenstates in the position basis are $$\lvert E_n\rangle\to \psi_n(x)=\...
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0answers
24 views

Quantum coherence as a thermodynamic quantity

Now that we know quantum coherence is one kind of resource that can be measured, is there any chance we can find some relation between quantum coherence and macroscopic thermodynamic quantity, just ...
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0answers
113 views

Computational scaling of quantum and classical Monte Carlo algorithms

How does the computational complexity of finding an equilibrium thermal state for a given Hamiltonian at a given temperature scale with system size under classical and quantum Monte Carlo? I know ...
2
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3answers
78 views

In quantum mechanics how can eigenfunction, eigenvalues, matrix methods give us values of real physical quantities? [closed]

Eigenfunction, eigenvalues, eigenstates & matrix methods used in quantum mechanics seems purely mathematical.How can they give us values of real physical quantities in quantum mechanics?
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3answers
68 views

Quantum computer able to compute non-computable elements? [closed]

I just recently read the journal article (below) about the Orchestrated Objective Reduction theory put forth by Roger Penrose and Stuart Hammeroff. According to this theory, the phenomenon of '...
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0answers
17 views

Interactions preserving separability

Consider the interaction (described by a unitary matrix U) of two qubits initially in a separable state |ab⟩ = |a⟩ ⊗ |b⟩, such that after interaction the composite system is in state U|ab⟩. Are there ...
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1answer
45 views

Can quantum computer provide random or just pseudo-random number, or none of both? [closed]

Can quantum computer provide random or just pseudo-random number, or none of both? It's a bit confusing me, since collapse of wave function once measured.
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1answer
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What is the difference between Quantum Gravity, Loop Quantum Gravity, Quantum Geometrodynamics, and Relativistic Quantum Mechanics? [closed]

What is the difference between Quantum Gravity, Loop Quantum Gravity, Quantum Geometrodynamics, and Relativistic Quantum Mechanics? As far as I know, they are all theories made to unify QM and GR. But ...
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1answer
54 views

Plotting hydrogen wave functions

This may sound a bit dumb but how do I plot the hydrogen wave functions? For example, what is exactly being represented [in this image][1]? Is it just the norm-squared of the wave function and is the ...
3
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2answers
87 views

Heisenberg uncertainty principle

In the double slit experiment, an electron interferes with itself and creates the pattern because it is in a superposition, traveling through both slits. If we place a detector at one slit, the wave ...
1
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1answer
48 views

Most probable radius of hydrogen in its ground state [closed]

I'm having trouble understanding how we do this. I know we must find the probability density function and then we can optimise it to find the most probable radius. I thought we would just take the ...
42
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9answers
6k views

Extension of Schrödinger's cat thought experiment

My question is quite simple. In the thought experiment of Schroedinger's cat: When the scientist measures the state of the cat, its wavefunction collapses into either the alive or dead state. But ...
4
votes
1answer
95 views

Energy Spectrum of Star Products

We have that a property of the transition operator defining c-equivalence (or star equivalence from equation 1 in Bertelson) is \begin{align*} T(f\star_Mg)=T(f)\star'T(g)\,, \end{align*} where $\...
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1answer
48 views

Examples of Matrix Product State(s)

Matrix product states(MPS) is a way of representing a (many-body) wavefunction. The method has been described in, https://arxiv.org/abs/1008.3477 However, would it be possible to see a concrete ...
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1answer
68 views

How to find the corresponding Hamiltonian in quantum, if Hamiltonian in classical mechanics is given? [closed]

Hamiltonian in classical mechanics is $$H=wxp $$ $x=$ position, $p=$ momentum coordinate. Find the corresponding Hamiltonian in quantum mechanics!
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0answers
28 views

Doubt regarding scattering and bound states in quantum mechanics

I just started studying quantum mechanics from Introduction to Quantum Mechanics by D. J. Griffiths. At the beginning of the second chapter, he proves that we cannot have negative energies in the time-...
4
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2answers
63 views

Half-integer angular momentum

Does half-integer angular momenta mean that the particle will always be found spinning? For example, if a particle is in a $l=\frac{1}{2}$ state, this means $ m=\pm\frac{1}{2}$ and since $L_z=\hbar m ...
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0answers
50 views

Gravitational analogue to the hydrogen atom

I'm not sure what to make of this problem from Griffiths' Intro to QM: Suppose the earth made a transition to the next lower level $(n-1)$. How much energy (in joules) would be released? What ...
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3answers
151 views

When we say electron spin is 1/2, what exactly does it mean, 1/2 of what?

When we say electron has spin of $\frac{1}{2}$, is that the value of the total spin of electron, or the projection on z axis, or the spin quantum number? When we say "electron has spin of $\frac{1}{2}...
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1answer
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What does it mean to have a transmission coefficient 1.03*10^-3

I solved a potential barrier problem. E=4.5ev V0=5eV barrier width a=950pm The transmission coefficient came out to be 1.03*10^-3 I was wondering what this means? isn't the transmission probability ...
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1answer
32 views

Is 3D optical lattice just a stack of 2D lattices?

I am confused about the idea of 3D optical lattice. Many papers use 3D optical lattice to study bosons behavior, but is it really a 3D system where atoms interact in all three directions or is it just ...