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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Writing operator evolution as a quantum dynamical map

In the Heisenberg picture we have the evolution of the operator in time given by: $$A(t)=U^+A(0)U$$ I was looking into the theory of open quantum systems where we introduce the concept of a quantum ...
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5 views

Does the dispertion medium affects Quantum Dots fluorescence efficiency?

I would like to use CdTe Quantum Dots to make a fluorescent coating on a transparent support. There's a link to the material here: ...
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12 views

Why is the energy shift due to a 'sagging' potential negative and independent of box size?

Consider a box of width $L$ and the composed of the following potential $$V(x)=V_0x(x-L), x\in[0,L]$$ and $V(x)=\infty$ elsewhere. Using perturbation theory - with a square box as the similar ...
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1answer
43 views

What gives a particle its identity?

A lot of very smart people have stitched together the standard model, and I accept it. I don't understand it, but I assume there should be a mechanism of sorts that gives a particle some fundamental ...
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1answer
48 views

Relativistic correction to Hydrogen atom - Perturbation theory

Given the relativistic correction $$ H_1' = - \frac{p^4}{8m^3 c^2} $$ to the Hamiltonian (i.e. a perturbation), what does it mean when $[H_1', \mathbf{L}] = 0$? The book I'm reading says this implies ...
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45 views

Can we have $E=0$ in Schrödinger's Equation?

I've read a little bit about zero-energy states, but I just don't get it. I'm just starting to study quantum mechanics and, at least for all the potentials I've seen until now (the most popular ones, ...
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22 views

Is this state an example of a separable state or an example of an entangled state? [on hold]

The Hong–Ou–Mandel effect also underlies the basic entangling mechanism in linear optical quantum computing, and the two-photon quantum state $\lvert 0,2 \rangle + \lvert 2,0 \rangle$ that leads to ...
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25 views

Why probability of detection by performing unambiguous quantum measurement is less than random guess in mesoscopic quantum regime?

In mesoscopic quantum regime (mean photon number 10000) and non-orthogonal coherent state(number of non-orthogonal coherent state 2000), why probability of detection by performing quantum unambiguous ...
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31 views

How to evaluate $[L^2,x_{j}]$

I want to evaluate the following commutator: $[\vec L²,x_{j}]$ where $\vec L= \vec x\times \vec p$, $(L_{i}=\epsilon_{ijk}x_{j}p_{k})$ and $\vec L²=L_{i}L_{i}$, here is my work so far: ...
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1answer
16 views

Mach-Zehnder probabilities

Where can I find the computations of probabilities for Mach-Zehnder experiments, say at the undergraduate level? For example I'm thinking of the type of experiments described at the beginning of David ...
7
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2answers
457 views

How can we know the state of a quantum system?

One of the postulates of QM states that given a system in a state $|\psi\rangle$ and given an observable $A$ whose eigenstates are $|\phi_i\rangle$, then the state of the system can be expressed as a ...
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1answer
43 views

Interpretations and approximations of uncertainty principle

Just a short question regarding an interpretation of the Heisenberg uncertainty principle $$\sigma_x \sigma_p \geq \frac{\hbar}{2}$$. Question: The uncertainty principle is sometimes written as ...
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0answers
29 views

Interpretations of uncertanity principle used for approximation

Just a short question regarding an interpretation of the Heisenberg uncertainty principle $\sigma_x \sigma_p \geq \frac{\hbar}{2}$. Question: Why is it also sometimes that $\Delta x$ and $\Delta ...
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5answers
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Does the observer or the camera collapse the wave function in the double slit experiment?

Ok so if we setup a camera before the slit we will find a single photon and will follow through accordingly, likewise by having a camera setup after the slit, we can retroactivly collapse the wave ...
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0answers
12 views

Stationary-state scattering process

In a stationary-state scattering process of an incoming plane wave, the outgoing spherical wave can be described by $\psi(\vec r) = e^{ikz} + f(\theta) \frac{e^{ikr}}{r}$. My question is, how is this ...
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2answers
537 views

Quantum entanglement definition [on hold]

How can we define Quantum entanglement (in QFT)? Can we regard it as organised information or just random data exchange? Why in either cases (Mathematically)?
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1answer
245 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 ...
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1answer
165 views

What is a Hulten potential?

What is the Hulten potential? (also spelled Hulthén, Hulthen, and Hultén.) When is it used? How is it derived? I vaguely heard about in the context of neutron synthesis / quantum mechanics.
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25 views

Specific function is a Linear combination of energy eigenstates

My lecturer made a statement: In the infinite square well potential $x\psi_n(x)$ (where $\psi_n$ is just the spatial part of an energy eigenstate) can be expressed as a linear combination of the ...
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130 views
+50

Condition for adiabatic approximation, derivation?

In quantum mechanics it is said that an adiabatic approximation is valid when $$T\gg \frac{\hbar}{\Delta E},$$ where $T$ is the time scale of variation of the Hamiltonian and $\Delta E$ is the typical ...
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1answer
34 views

Interaction Hamiltonian coupling question

System is composed of two qubits and the bath is one bath qubit. The interaction Hamiltonian is: $$\sigma_1^x\otimes B_1 + \sigma_2^x\otimes B_2$$ where $B_i$ is a 2 by 2 matrix. I try to interpret ...
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3answers
56 views

Mathematical treatment of electron double slit experiment

Can someone please provide me with the mathematical treatment of the double slit experiments with electrons? The diffraction pattern seems to resemble that generated by photons (light) counterpart, ...
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0answers
34 views

The quantum state measurement in the eigenbasis of unknown hamiltonian

Let's say we have some physical system in the unknown hamiltonian $H$, which can be represented with the sum of Pauli matrices. For one two-level system it can be set as $H \propto \vec{n}\vec\sigma$, ...
7
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4answers
398 views

Is it possible for $\Delta x$ ($\sigma_x$) of any free particle wave packet to be decreasing at any time?

Consider any wave packet describing a free particle (so no potential or other forces acting on it). Then it can be shown that $\Delta p$ does not change in time. However, my question is what happens ...
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1answer
47 views

Representing operators in the Glauber-Sudarshan P-representation

If $| \alpha >$ represents a coherent state (the normalized right eigenstate of the destruction operator $a$ in Quantum Mechanics; $\alpha$ is a complex number), then it is known that: ...
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51 views

Relating purity of reduced density matrix to concurrence [on hold]

Given the initial quantum state: $$ |\psi\rangle=\alpha|0\rangle+\beta|1\rangle $$ If I perform the CNOT operation: I get the two cubit state: $$|\Psi'\rangle=\alpha|00\rangle+\beta|11\rangle \ ...
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1answer
57 views

Time-ordering of fermion operators

If $A$ and $B$ are fermion operators then the time ordering is defined as \begin{eqnarray} T(AB) = \left\{ \begin{array}{rl} AB, & \mbox{if $B$ precedes $A$}\\ -BA, & \mbox{if $A$ precedes ...
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2answers
68 views

Calculating the expectation value of spin [on hold]

Consider the state-space with a base formed by the eigenstates of the operator $\hat{S}_z$. For the state $|\phi\rangle=\frac{1}{\sqrt2}|+\rangle_z-\frac{1}{\sqrt2}|-\rangle_z$, what is the value ...
4
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2answers
585 views

What is the difference between realism in locality, and counterfactual definiteness?

I understand the EPR-experiment and the Bell inequalities. I can see how dropping 'locality' solves the issue, and how dropping 'realism' solves the issue (e.g. there are really no hidden variables ...
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1answer
4k views

How is multiplicity given by 2S+1?

Suppose there are two electrons in an atom with $s_1 = \frac{1}{2}$, $l_1 = 1$ and $s_2 = \frac{1}{2}$, $l_2 = 1$. Hence the total $S$ (of the atom) may be +1 or 0. And total $L$ is either $+2$, $+1$ ...
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1answer
72 views

How to manipulate higher spin systems (higher than spin 1/2) using a given operator?

I’ve been reading ¨Halzen, F., and A. D. Martin. Quarks and Leptons. New York: Wiley Text Books, January 1984. ISBN: 9780471887416¨, and I’d like some clarification of a concept, please: I’m ...
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2answers
72 views

Geiger counter in the Schrodinger's cat experiment

Inside the Schrodinger's cat's box, the moment the radiation is detected by the counter, doesn't this mean the system already has a fixed eigenstate (a collapsed wave function, or is decoherent, ...
1
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2answers
50 views

Can AMO physics be applicable for space travel? [on hold]

I know it sounds very stupid question. I am a Ph.D student currently working on the AMO physics (Quantum Optics). I recently saw articles about the Spacex, and I thought it is really amazing, and ...
2
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4answers
105 views

When to use Quantum Mech.? [on hold]

Is there any parameter (in terms of physical quantities such as mass, length, charge...) which can be used to decide when to treat a system quantum mechanically and not classically?
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0answers
18 views

Clarification: non-relativistic fine structure of a one-electron atom

The fine structure energy shift (in the non-relativistic limit) for a single-electron atom due to spin-orbit coupling is given by $$\Delta ...
0
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1answer
26 views

Uncoupled and coupled bases for electrons in hydrogen atom?

I'm given that for an electron in a hydrogen atom, $L=2$ and $S=1/2$ (quantum numbers associated with $L^2$ and $S^2$). I'm also given that for the uncoupled representation, the basis function is ...
3
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1answer
40 views

Constructing a POVM to discriminate $m$ quantum states. What if they're linearly dependent?

I've come across this problem in Nielsen & Chuang's Quantum Information book (problem 2.64) Suppose Bob is given a quantum state chosen from a set $|ψ_1 \rangle, . . . , |ψ_m\rangle$ of linearly ...
10
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5answers
2k views

Why don't we use the concept of force in quantum mechanics?

I'm a quarter of the way towards finishing a basic quantum mechanics course, and I see no mention of force, after having done the 1-D Schrodinger equation for a free particle, particle in an ...
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0answers
24 views

Variational Method for one dimensional infinite square well [on hold]

I have an one dimensional infinite square well of width $a=1$, and I want to use variational method to produce the ground state energy. My trial wavefunction is ...
1
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0answers
10 views

Why the bandgap of inorganic semiconductors decreases with temperature?

The temperature dependence of the energy bandgap in inorganic semiconductors is given by $$E_g (T) = E_{g,0} - \frac{\alpha T^2}{T+\beta}$$ where $\alpha, \beta$ are both positive, and the (somewhat ...
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0answers
13 views

Classical space-time and quantum indiscernibility [on hold]

Non-relativistic QM works in Newtonian space-time. Does the representation of a quantum system in this setting individualizes it in such a way that this conflicts with the non-individuality and the ...
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0answers
26 views
0
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27 views

Rotation operation on spin-1/2 particles

How does rotation operators work on a particle? What does it do on the particle conceptually? Also does particles spin on its axis?
3
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2answers
2k views

Coupled quantum harmonic oscillator

Given the following Hamiltonian for two identical linear oscillators with spring constant $k$ and interaction potential $\alpha x_1x_2$; I was asked to find the expectation value $\langle ...
4
votes
3answers
944 views

Are quantum mechanics and general relativity predictions of string theory, or were they built into the theory from the start?

Are quantum mechanics and general relativity predictions of string theory, or were they built into the theory from the start? If the former, why aren't tests of GR and QM considered simultaneous tests ...
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26 views

Meaning of Hamiltonian between two different states

If we have states $\left | 1 \right>$ and $\left | 2 \right>$, and the Hamiltonian operator $\hat{H}$, what is the meaning of the expression $$\left< 1 \right | \hat{H} \left | 2 \right ...
2
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1answer
47 views

Using symmetry to determine a hydrogen electron's decay route from $|300\rangle$ to $|100\rangle$

Lets say we have an electron in state $|nlm\rangle = |300\rangle$ of the hydrogen atom. By selection rules, we know that it can only decay to ground state in 3 ways, namely through the $|21m\rangle$ ...
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1answer
51 views

Expectation value [on hold]

Which of the following equations is correct? why?
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18 views

Construct recurrence relation for the temporal evolution of a Master equation

Say that we have a system evolving over discrete timesteps. The quantity we are interested is X and is given by a distribution $P_X$. This distribution is evolving temporally, and we have a ...