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

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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0answers
26 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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0answers
54 views

Is it almost impossible to separate two point charges stuck together?

$$F=k\frac{qQ}{r^2},$$ if $r\rightarrow 0$ then $F\rightarrow \infty$.
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0answers
37 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 $H \propto \vec{n}\vec\sigma$, ...
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0answers
38 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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2answers
567 views

Quantum entanglement definition [on hold]

How can we define Quantum entanglement (in QFT)? What are the known mathematical settings and special physical (or logical) conditions of QE applied to Quantum computing?
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2answers
465 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
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 ...
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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 ...
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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 ...
2
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4answers
108 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
11 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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3answers
58 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
14 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

Rotation operator adjoint multiplication [on hold]

Why does the last term equal 0(d$\phi^2$)?
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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 ...
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0answers
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?
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0answers
27 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 ...
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0answers
56 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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0answers
19 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 ...
3
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1answer
42 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 ...
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0answers
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 ...
5
votes
1answer
62 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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1answer
53 views

Quantum Mechanics: Rotation operators

How do I know what direction of the rotation operator to use on the initial state of a spin-1/2 particle? For example, a spin-1/2 particle initially in the $\lvert y \rangle$ state enters a SGz ...
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2answers
51 views

Can AMO physics be applicable for space travel? [closed]

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 ...
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1answer
23 views

relativistic temperatures energy assumptions

why is the assumption $k_bT>>mc^2$ made for relativistic temperatures, where did the kT come from and how is it related to mc^2?
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54 views

Can anyone explain that “the human body is made of energy (photons)”? and how many photons it contains?

The modern research has shown that our body is basically made of energy not matter in a sense that atom itself is basically consists of energy waves, so it is nothing but energy. How we can explain ...
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1answer
33 views

Where can I learn about band theory?

I'm studying quantum mechanics and I want to understand perfectly where the bands of the electronic sturcture come from. I've read that it is related with the periodic potential, Bloch waves and ...
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0answers
12 views

Time variable double slit single photon interference

Has the double slit, single photon interference experiment ever been performed where time is a variable, ie. one photon emitted per day? Would the interference pattern emerge?
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2answers
39 views

Particle in a box, quantization of energy

I'm learning about how the energy of matter is quantized like how the energy of light is. My textbook illustrates the concept of quantization with the particle in a box: "A particle of mass $m$ ...
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0answers
16 views

Are there any specific examples of the application of Lewis-Riesenfeld procedure to time dependent Hamiltonians in QM?

Lewis-Riesenfeld invariant theory is a theory applicable to solve time-dependent Schrodinger equations. I have always encountered the theory related to the procedure, however never encountered any ...
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1answer
54 views

Expectation value [closed]

Which of the following equations is correct? why?
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1answer
22 views

Under what conditions does a beam splitter entangle two input photons?

There is a dispute on PhysicsForums related to what are the conditions necessary for two photons to be entangled by a beam splitter. Lots of references given by the forum users but they never arrive ...
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3answers
100 views

Why is $np$ always equal to $n_i^2$?

For you guys who studied semiconductor physics must be familiar with the equation: $$np=n_i^2$$ I can understand why this is true for the intrinsic case (the broken bonds would always provide ...
1
vote
1answer
42 views

Show the Berry phase is invariant under $U(1)$ unitary transform [closed]

Recall that $$\gamma_n = \oint A_n(R) \cdot dR = \oint \langle\psi_n(R)|i\nabla_R|\psi_n(R) \rangle \cdot dR.$$ Under the $U(1)$ transform, $$\psi_n \to \psi'_n \equiv e^{i\xi_n(R)}\psi_n,$$ where ...
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0answers
24 views

Production of entangled photons by spontaneous down conversion [closed]

I have found that the conditional uncertainty product of position and momentum of any one photon produced in the spontaneous parametric down conversion process using a gaussian pump beam decreases ...
2
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0answers
27 views

Kitaev chaing, time reversel symmetry, particle hole symmetry

I was wondering if the Kitaev chain has time reversal symmetry. I think it probably doesn't because by staking Kitaev chains it is possible to create a so called Chern insulator with propagating ...
2
votes
1answer
52 views

Decoupling coupled differential equations in dynamically coupled two state system

Consider the following dynamically coupled two state hamiltonian, $$H=-B\sigma_z-V(t)\sigma_x.$$Taking the eigenfunctions of $\sigma_z$ ($|+>$ and $|- >$) as basis vectors, we have the wave ...
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0answers
39 views

How many observations over an atom can be made?

In order to determine the orbitals of any unknown atom , is it possible to make and record direct observations of electrons around the atom without disturbing the atom ? How many observations can one ...
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0answers
16 views

What is Loewdin downfolding method?

I am a student in solid state physics. I wonder if somebody could explain the mathematical background of downfolding method that is often used by Ole K. Anderson. Which restriction (conditions) to ...
0
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0answers
32 views

Solving Schrodinger's Equation in Bunimovich Stadium Boundary Condition [closed]

I need to solve, as mentioned, Schrodinger's equation in a Bunimovich stadium-shaped infinite potential well with Dirichlet BC Numerically (this isn't possible analytically). In order to do so, I need ...
4
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2answers
120 views

Does QM unequivocally violate the law of bivalence?

I had heard that QM violates the law of bivalence. Does anyone claim that?
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2answers
94 views

Unitary operators evolving the set of Pauli matrices

Consider the Heisenberg picture of Quantum Mechanics. For a two state system we have the Pauli matrices evolving according to the relation $$\sigma_i(t)=U^+\sigma_i(0)U$$ where $U=e^{-iHt/\hbar}$ and ...
0
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1answer
62 views

Quantum Mechanics: how exactly does “delta function normalization” work for eigenfunctions in 1-d free space case?

The definition of "delta function normalization" says a basis of eigenfunctions of a particle in free space are orthonormal when ...
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2answers
44 views

Order of operators and numbers inside a bracket

I had an argument with my professor. Let $H$ be an operator (e.g. hamiltonian). Let capital $X$ denote the position operator. Let $f$ and $g$ be functions of $X$ that do NOT commute with $H$. Now ...
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1answer
32 views

Measuring compatible observables in quantum mechanics

Suppose a particle that is under a quantum oscillator potential and is, initially, in the state $\Psi(x,0)=\frac{1}{\sqrt3}\phi_1(x)+\sqrt{\frac23}\phi_2(x)$, where $\phi_1(x)$ and $\phi_2(x)$ are ...
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0answers
48 views

Single particle diffraction: how is this possible?

The intensity distribution of diffraction patterns are typically explained by looking at points of constructive and destructive interference of the diffracted waves on the detector. These diffracted ...
2
votes
1answer
64 views

Diagonalisation: Schmidt vs eigenvalue - when to use which?

In physics we encounter diagonalisation of matrices or operators in a variety of areas. But there are different kinds, the main two being Schmidt decomposition and eigenvalue diagonalisation. The two ...
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1answer
22 views

Is linear polarization of entangle photons in 2-particle decay always correlated?

In Aspect's paper "Bell's Theorem: The naive..." and in an 2002 AJP article by Dehlinger and Mitchell "Entangled photon apparatus..." the photons are described to be in the $|xx\rangle+|yy\rangle$ ...
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23 views

Relative motion in particle measurements

I was thinking about measurement of particles at almost-zero energies/temperatures and the movement associated with it. Compared to an observer next to the particle who sees the particle moving at ...