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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405 views

A proton is trapped in an infinitely deep well of L meters. The proton is in the first excited state. How does the excited state change the question.

The real question was: A proton is trapped in an infinitely deep well of 1*10^-14m. I suppose that is unimportant as that should only help us decided the limits of our integration. What I'm worried ...
2
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4answers
943 views

what is it called: box potential with one infinite wall

The finite square well and the infinite square well problem are well known, however is there a reason that there is almost no reference to the one sided infinite square well? Consider a particle ...
2
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0answers
105 views

How can one trace out polaritonic degrees of freedom?

I have read the paper "Steady state entanglement between hybrid light-matter qubits", arXiv:0711.1830v2. There, writers obtained density operator in matrix form after solving steady state equation ...
1
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2answers
574 views

Radar Frequency Bandwidth

I've come across an interesting question in the course of doing some exam review in a quantum mechanics book and thought I'd share it here. "What must be the frequency bandwidth of the detecting and ...
4
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2answers
851 views

Use of Operators in Quantum Mechanics

I understand the form of operators in use for quantum mechanics such as the momentum operator: $$\hat{\text{P}}=-ih\frac{d}{dx}$$ My question is in what ways can I use it and what am I getting back? ...
4
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1answer
81 views

Spekkens Toy Model, Internal Comonoids

I have been thinking about Spekkens Toy model in terms of interfaces. The Spekkens paper concerns a physics based on only being able to receive answers to half the number of questions necessary to ...
29
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8answers
3k views

Why $\displaystyle i\hbar\frac{\partial}{\partial t}$ can not be considered as the Hamiltonian operator?

In the time dependent Schrodinger equation $\displaystyle, H\Psi = i\hbar\frac{\partial}{\partial t}\Psi$ , the Hamiltonian operator is given by $\displaystyle H = -\frac{\hbar^2}{2m}\nabla^2+V$ ...
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1answer
104 views

Number of conditions for a two-particle state to be decomposable

Suppose we have a general two-particle state $ \Phi (x_1, x_2 ) = \sum_{n_1,n_2} \phi_{n_1,n_2}(x_1,x_2)|n_1,n_2> $, where $n_1$ can be any of $n$ possible states, and $n_2$ can be any of $m$ ...
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2answers
1k views

The mathematics of entanglement

I've finally managed to get a grasp on the Bell test experiments and all that they imply about our reality. Now I'm curious about the mathematical derivation which allowed Schrodinger to predict the ...
4
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2answers
199 views

Does a finite wave necessarily have to be non-monochromatic in reality?

Does a finite wave necessarily have to be non-monochromatic in reality, or is that implication just a result of the mathematical analysis? I always wonder at these sort of things that come out of a ...
2
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2answers
524 views

Has anyone actually “seen” entanglement?

I want to know if the following has been done experimentally; after the spin (or any other characteristic with a probability of 50%) of 2 entangled particles has been measured, we change the spin of ...
3
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3answers
685 views

Hamiltonian with position spin coupling

I am solving a Hamiltonian including a term $(x\cdot S)^2$. The Hamiltonian is like this form: \begin{equation} H=L\cdot S+(x\cdot S)^2 \end{equation} where $L$ is angular momentum operator and $S$ is ...
4
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1answer
91 views

Convexity — reference request

I've been reading a few papers on generalized probabilistic theories, and have been struggling through proofs of some results that involve use of convexity and group theory, e.g. this paper on bit ...
9
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3answers
374 views

Hilbert-Schmidt basis for many qubits - reference

Every density matrix of $n$ qubits can be written in the following way $$\hat{\rho}=\frac{1}{2^n}\sum_{i_1,i_2,\ldots,i_n=0}^3 t_{i_1i_2\ldots i_n} ...
2
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1answer
327 views

Angular Momentum Operator

I'm looking at a review question I was given and it quite frankly has me stumped. "Using matrix representations find $L^{3}_{x},L^{3}_{y},L^{3}_{z}$ and from these show that $L_{x}, L_{y},L_{z}$ ...
7
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1answer
160 views

How does one geometrically quantize the Bloch equations?

I've just now rated David Bar Moshe's post (below) as an "answer", for which appreciation and thanks are given. Nonetheless there's more to be said, and in hopes of stimulating further posts, I've ...
2
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1answer
346 views

Expected number of quanta in harmonic oscillator states

I'm working my way through A Squeezed State Primer, filling in details along the way. Let $a$ and $a^\dagger$ be the usual annihilation and creation operators with $[a,a^\dagger]=1$ and ...
1
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1answer
443 views

Differential Equation in Spherical Harmonics Derivation

I've been reviewing derivations of the spherical harmonics in quantum mechanics; mostly as review but also to make sure I understand where the concepts arise from. However, every derivation I've ...
12
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4answers
946 views

Rigorous proof of Bohr-Sommerfeld quantization

Bohr-Sommerfeld quantization provides an approximate recipe for recovering the spectrum of a quantum integrable system. Is there a mathematically rigorous explanation why this recipe works? In ...
16
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5answers
831 views

Is quantum mechanics intrinsically dualistic?

In just about every interpretation of quantum mechanics, there appears to be some form of dualism. Is this inevitable or not? In the orthodox Copenhagen interpretation by Bohr and Heisenberg, the ...
2
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1answer
73 views

Does frequentism require exponentially many trials in some cases?

Frequentism is the philosophy that probabilities are statistical in the sense that they give the limiting frequency ratios of outcomes as the number of trials is large enough. For tiny probabilities ...
11
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5answers
2k views

Consequences of the new theorem in QM?

It seems there is a new theorem that changes the rules of the game in the interpretational debate on QM: http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392 Does this only leave ...
2
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3answers
457 views

What is the rationale behind representing a state function by a complex valued function in QM?

What is the rationale behind representing a state function of an electron with a complex valued function $\Psi$. If only the probabilistic argument was required then why not represent it with just a ...
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0answers
2k views

Experimental test of the non-statisticality theorem?

Context: The paper On the reality of the quantum state (Nature Physics 8, 475–478 (2012) or arXiv:1111.3328) shows under suitable assumptions that the quantum state cannot be interpreted as a ...
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2answers
139 views

Equivalence between Differential Geometry and Mechanics?

Given a metric $$ ds^{2}~=~ g_{a,b}dx^{a}dx^{b}. $$ Here Einstein's summation convention is assumed for $a$ and $b$. Then given the Laplacian over that metric, can then we find a metric $ ...
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1answer
469 views

Phase shift for Scattering in radial potentials

given a radial potential in 3 dimension and its Schroedinguer equation $ -D^{2}U(r) + \frac{l(l+1)}{r^{2}}+V(r) $ here D means derivative with respect to 'r' then if we apply quantum scattering how ...
3
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8answers
731 views

Does the wave function/density state actually exist?

I have been reading with interest the debates here on whether the wave function/density state actually collapses or not, or whether it is subjective Bayesian or objective with actual complex numbered ...
5
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2answers
269 views

Are there irreducible tensors of half integral degree in quantum mechanics?

According to Ballentine, an irreducible tensor of degree k can be defined as a set of $2k + 1$ operators $\{T_q^{\;\;(k)}:(-k \le q \le k)\}$ satisfying the following commutation relations: $$ ...
3
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1answer
184 views

Distinguishing two quantum states practically

Suppose we have two states $$|x\rangle = 1 |0\rangle + 0 |1\rangle$$ and $$|y\rangle = \sqrt{1-\epsilon^2} |0> + \epsilon |1>$$ where say $\epsilon = 10^{-20}$ Can we distinguish ...
5
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2answers
666 views

How can we be sure that nature isn't “faking” quantum statistics?

In a recent publication, Experimentally Faking the Violation of Bell’s Inequalities (Gerhardt 2011) (arXiv version), the statistics of quantum mechanics is faked using classical light sources. But if ...
5
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2answers
1k views

Canonical momentum in different coordinate system

The canonical momentum is defined as $p_{i} = \frac {\partial L}{\partial \dot{q_{i}}} $, where $L$ is the Lagrangian. So actually how does $p_{i}$ transform in one coordinate system $\textbf{q}$ to ...
5
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0answers
196 views

What happens to a Luttinger liquid under time reversal?

Suppose you a have an ordinary Luttinger liquid with $$ H = \int dx \sum _{\eta= \pm 1 , \sigma =\uparrow,\downarrow } \psi^\dagger_{\eta, \sigma} (x) (-i v \eta \partial _x) \psi _{\eta,\sigma} (x). ...
10
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1answer
80 views

Accurate quantum state estimation via “Keeping the experimentalist honest”

Bob has a black-box, with the label "V-Wade", which he has been promised prepares a qubit which he would like to know the state of. He asks Alice, who happens also to be an experimental physicist, to ...
6
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3answers
757 views

Lorentz force in Dirac theory and its classical limit

It is well known that in Dirac theory the time derivative of $P_i=p_i+A_i$ operator (where $p_i=∂/∂_i$, $A_i$ - EM field vector potential) is an analogue of the Lorentz force: $\frac{dP_i}{dt} = ...
3
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1answer
401 views

Proca theory and renormalization

What is the simplest physical argument to claim that Proca theory (involving a massive spin-1 boson) is not renormalizable?
6
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2answers
977 views

Equation of motion for the reduced density matrix

The equation of motion for the density matrix of a many body isolated quantum system is the von Neumann's equation: $\dot{\rho }(t)=i[\rho (t),H]$. How about the equation of motion for the reduced ...
2
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1answer
768 views

Simplified partial trace of two operators

If I have two operators A and B living in the Composite Hilbert Space $H_I \bigotimes H_{II} $ and I want to take the partial trace of $C=AB$ over the subspace $H_I$, i.e., $Tr_I[AB]$, is there any ...
7
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1answer
164 views

Quantum mechanical gravitational bound states

The quantum mechanics of Coloumb-force bound states of atomic nuclei and electrons lead to the extremely rich theory of molecules. In particular, I think the richness of the theory is related to the ...
4
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1answer
255 views

Lifetime of a quasiparticle

I'm having a rather technical question concerning the calculation of the lifetime of a quasiparticle. The reference I use is: ...
6
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2answers
1k views

In layman's terms, what is a quantum fluctuation?

What causes it and how does it occur? If you do post some mathematics, please explain what each term means too please.
4
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3answers
905 views

Planetary model of atom still valid?

When I was in school, I learned (from Democritus) that an atom was similar to a solar system, with the nucleus being the sun, and the electrons being the planets. Of course, there are some ...
0
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2answers
213 views

Speed Distribution of The Particles

I want to know the distribution of the particles's speed. The particles what I mean are nucleons and electrons of element. Consume there is 1kg of iron on room temperature and it's shape is sphere. ...
13
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5answers
22k views

What is the math knowledge necessary for starting Quantum Mechanics?

Could someone experienced in the field tell me what the minimal math knowledge one must obtain in order to grasp the introductory Quantum Mechanics book/course? I do have math knowledge but I must ...
13
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4answers
1k views

Energy is actually the momentum in the direction of time?

By comparatively examining the operators a student concludes that `Energy is actually the momentum in the direction of time.' Is this student right? Could he be wrong?
0
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1answer
3k views

Definition of “localized state”

Is there a definition of a localized state in quantum mechanics? I've seen that some textbooks use this term, but they don't give a definition. Thanks
10
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1answer
1k views

What are the specific requirements for a do-it-yourself quantum double-slit experiment?

I was shocked to recently learn that the double-slit experiment is not only possible to do with completely ordinary equipment (with photons of course), but it actually looks rather easy. This is from ...
2
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1answer
538 views

How many different formulations of QM currently exist?

I read some while ago that, currently, eleven different formulations of quantum mechanics exist. Is this correct / accurate? If yes, can someone provide a pointer(s) (i.e. link(s)) to the various ...
6
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1answer
172 views

Quantum mechanics as a Markov process

I am currently involved in some understanding on this matter with a colleague of mine. I know all the literature about but I do not know the state of art. Please, could you provide some relevant ...
3
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2answers
345 views

Quantum Mechanics Video lectures

Are there any good video lectures for learning quantum mechanics at the level of Griffith?
8
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5answers
2k views

Why Negative Energy States are Bad

The argument is often given that the early attempts of constructing a relativistic theory of quantum mechanics must not have gotten everything right because they led to the necessity of negative ...