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 ...

learn more… | top users | synonyms (3)

2
votes
5answers
24 views

Expectations values of position in quantum mechanics

In quantum mechanics, we can show that $$ \langle r \rangle^{-1} \neq \langle r^{-1} \rangle $$ I can understand this mathematically as the integrals are different but can anyone explain physically - ...
1
vote
2answers
80 views

Two soft questions about spin and the particle nature of electrons

How can we define spin as the spin of an electron around it's own axis if an electron is described by a probability cloud of finding an electron in a point in space? How does that probability cloud ...
0
votes
1answer
23 views

What is a good book for quantum mechanics and quantum computation? [duplicate]

I am looking for a book in quantum computers for self-learning.The kind of book that teaches quantum-mechanics + quantum-computation. I have basic understanding in calculus , linear-algebra (like ...
2
votes
2answers
196 views

Why does electron move in an elliptical path?

According to Sommerfeld's atomic model, an electron moving around a central positively charged nucleus is influenced by the nuclear charge. As a result of which, the electron moves in an elliptical ...
1
vote
0answers
53 views

An Operator Identity relating to Trace [duplicate]

Suppose that $\hat H$ is an operator (typically a Hamiltonian) and $\beta$ is a positive parameter (typically $\beta=1/k_BT$). Show that $$ \mathbf{Tr}\Big(e^{-\beta\hat H}\Big) \geq ...
0
votes
1answer
14 views

Fine Structure Degenerate Perturbation Theory Hydrogen

Note: We are dealing with perturbation on the states $|nlm_lm_s>$ where n is the principle quantum number, l is the angular momentum quantum number, and $m_l$ and $m_s$ are the eigenvalues of $L_z$ ...
0
votes
0answers
33 views

Proof that the trace ${\rm tr}(\rho^2)=1 $ of the square of a pure state density matrix $\rho$ is always one [on hold]

Can someone provide a proof that the trace ${\rm tr}(\rho^2)=1 $ of the square of a pure state density matrix $\rho$ is always one?
0
votes
1answer
43 views

A few questions on wave packets and uncertainty relations

According to Cohen-Tannoudji the wave-function for a one-dimensional free particle can be written as $$ \psi (x,0)=\frac{1}{\sqrt{2 \pi}} \int g(k) e^{ikx} dk.$$ While $g(k)$ is not specified, there ...
0
votes
0answers
14 views

Dicke states, spin squeezing and quantum metrology

Dicke states are by definition simultaneous eigenstates of the $J_z$ and $J^2$ operator. What is the difference between these states and Dicke squeezed (DS) states? I know that these are "entangled" ...
-1
votes
0answers
41 views

Why most problems encountered in quantum mechanics cannot be solved exactly?

Exact solutions of the Schrödinger equation exist only for a few idealized systems. Why most problems encountered in quantum mechanics cannot be solved exactly?
1
vote
1answer
47 views

If electrons aren't revolving around the nucleus, why do atoms have orbital magnetic moment?

In most introductory textbooks, the explanation of orbital magnetic moment is based on Bohr's model and electrons orbiting around the nuclues, which can be modeled as a current loop. For example, ...
2
votes
0answers
36 views

A quantum mechanical description of a polarizing filter

When a single photon with polarization $\mathbf{a}$ arrives at a linear polarizing filter in the direction $\mathbf{p}$, the photon has a probability of $(\mathbf{a}\cdot\mathbf{p})^2$ to pass through ...
0
votes
0answers
42 views

How to read this state in quantum physics?

I am having a little trouble understanding this state: $$ \,^3D\left[3/2\right]_{1/2} $$ What does the $[3/2]$ indicate here?
2
votes
2answers
49 views

Leakage of X-ray radiation

Suppose a sample of strontium-90 is stored in a lead container with lead walls. It is know that X-ray radiation may be detected outside the lead container. After some discussion with my peers, it ...
3
votes
1answer
60 views

Does there exist a state for which $\Delta\sigma_x^2=\Delta\sigma_y^2=0$? If not, how does one prove it?

I just realized that the uncertainty principle says that $$\Delta\sigma_x^2 \Delta\sigma_y^2 \ge \left(\overline{\hat\sigma_z}\right)^2,$$ where ...
0
votes
1answer
27 views

Uncertainty principle in Harmonic Oscillator

In a single particle Harmonic Oscillator, suppose I prepare it in the ground state and then measure its position. From the relation connecting Total Energy, Kinetic energy and Potential I can ...
4
votes
1answer
67 views

Why can we leave off half of the general solution?

In these pdf notes, it says at the bottom of the first page and beginning of the second: [...] whose solution is: $$\Psi(\theta) = c_1 e^{i\omega\theta} + c_2 e^{-i\omega\theta}$$ Since we are ...
0
votes
1answer
40 views

Correct approach for calculating excited states of circular quantum dot under effective mass approximation

From Asnani, Mahajan et al, Pramana Journal Of Physics 73 #3 (2009) p574-580 "Effective mass theory of a two-dimensional quantum dot in the presence of magnetic field", which can be seen here: ...
1
vote
1answer
146 views

Particle Outside the Box

What prohibits, mathematically, that a particle cannot be found outside the box ? Here, I am referring to particle in a box problem (infinite potential on both ends & zero potential along the ...
1
vote
3answers
148 views

Classical Hamiltonian involving product of factors whose quantum analogues don't commute

Dirac remarked in his quantum mechanics book: One can usually assume that the Hamiltonian is the same function of the canonical coordinates and momenta in the quantum theory as in the ...
4
votes
2answers
333 views

Where to place the operator?

I believe it's standard to place the operator in between the conjugate of the wavefunction and the wavefunction itself. For instance, $$\langle p\rangle = \int_{-\infty}^{\infty}\Psi * ...
4
votes
2answers
79 views

How does electron spin change instantaneously without violating inertia principle?

The inertia in one of the main properties of matter. That is why all process in macro world do not happen instantaneously. What I do not understand is how we should apply this general idea of inertia ...
3
votes
1answer
122 views

Is there only radial motion in the Hydrogen ground state?

The ground state of the Hydrogen atom is spherically symmetric. In other words, the wave function Psi depends only on the distance r of the electron from the nucleus. As a consequence all ...
3
votes
2answers
92 views

Why is $\hat{p} \circ \hat{p}$ the operator corresponding to $p^2$?

I understand from several heuristic arguments that in one dimension, the quantum-mechanical operator $\hat{p} = -i\hbar\,\partial_x$ corresponds to the classical momentum $p$, in the sense that a ...
1
vote
1answer
38 views

Uncertainty in position and kinetic energy

How do you find the uncertainties for $x$ and $K$? Knowing that the general uncertainties = $$ \sigma_A \sigma_B \geq 1/2\int \psi ^*[\hat A,\hat B] \psi dx\, $$ I figured out the commutator, for ...
2
votes
1answer
111 views

Normalizing wavefunction

If you are trying to normalize $\psi = A\sin kx$, and you find that $|A|^2 = \frac{2}{a}$, why do you take the positive square root and not the negative? What happens if you take the negative square ...
2
votes
1answer
47 views

Are there any experimental tests of non-locality / Bell inequalities that do not rely on spin?

All the experiments I know, which have been performed to test Bell inequalities, are somehow based on measuring the spin degree-of-freedom of some particle (usually photons, sometimes electrons). I ...
1
vote
2answers
54 views

Could a trial wavefunction providing exact eigenenergy differ from the exact eigenfunction by a zero measure function?

Given the eigenequation of a Hamiltonian $$ H |n \rangle = E_n |n \rangle \tag{1} $$ We write it in the position representation $$ \langle x | H | n \rangle = E_n \langle x | n \rangle \tag{2} $$ ...
1
vote
2answers
103 views

What is the expectation value of the 3D delta function for the Hydrogen atom ground state?

I'm trying to evaluate the expectation value of some perturbation Hamiltonian $$H=\alpha \delta^3(\vec{r}),$$ where $\alpha$ is a positive constant, for the ground state wavefunction of the hydrogen ...
0
votes
0answers
28 views

Problem in Solving an Equation in Quantum Mechanics [duplicate]

I am trying to reproduce this paper : http://www.ias.ac.in/pramana/v73/p573/fulltext.pdf But, somehow I am stuck at equation (7). The equation that I am trying to solve for particle outside the well ...
1
vote
0answers
90 views

Forced Quantum Harmonic Oscillator

I'm just starting my journey to QFT and Particles physics and I have a question about the problem of QHO witch we hit with a force $F(t)$ for $ t< t' $, for which the force is zero for $t>t'$. ...
-1
votes
0answers
21 views

Commutator of $SU(2)$ angular momentum operators [on hold]

Prove the following statement. $$[J_i,J_j] = i\hbar\epsilon_{ijk}J_{k}$$ using rotation operators.
0
votes
0answers
12 views

Deriving (spatial) angular momentum selection rule [on hold]

I am having a go at Problem 7.21 from Binney and Skinner's The Physics of Quantum Mechanics. Here's the first half of the problem: Here is my attempt at the moment: $$[ L^{2}, [L^{2}, x_{i}] = [ ...
1
vote
1answer
36 views

Time energy uncertainty principle [duplicate]

$ \sigma _{H}\sigma _{Q}\geqslant \frac{h}{4\pi }\frac{d\left \langle Q \right \rangle}{dt}$ $\Delta E = \sigma _{H}$ $\Delta t = \frac{\sigma _{Q}}{d\left \langle Q \right \rangle / dt}$ $\Delta E ...
1
vote
0answers
31 views

Where Does the Exponent Come From in the Expression for the Rotation Operator

I am currently reading John S. Townsend's "A Modern Approach to Quantum Mechanics." In section 2.2 he introduces the $\hat J$ operator, which he refers to as "the generator of rotations." He gives the ...
1
vote
2answers
134 views

QFT Hilbert spaces over other rings than the complex numbers $\mathbb{C}$

I would like some help evaluating a physics theory recently proposed by a physics professor at the College of Dupage. I think the theory is utterly wrong, for very simple reasons. If an amateur ...
1
vote
0answers
26 views

How can a photon exist on its own without a mass? [duplicate]

For example, thermal energy exists and has no mass, but is carried by particles which have mass. A photon is described as a particle - how can a photon exist on its own, travel in space and even push ...
4
votes
0answers
87 views
+50

Does tunneling transmission probability depend on the density of states or velocity?

In some quantum text books [1], the tunneling transmission formula depends only on the density of states of 2 regions (DOS) involved in tunneling. ($T(E) = C \times DOS_1(E) \times DOS_2(E)$, where C ...
0
votes
1answer
57 views

Two quantum observers

It is considered that a quantum mechanics parameter is undefined until it is measured.But what happens if two independent observers measure the same quantum parameter? Do they get the same value or ...
8
votes
2answers
479 views

Trouble understanding the Bohr model of the atom

In this article it says: The electrons can only orbit stably, without radiating, in certain orbits (called by Bohr the "stationary orbits") at a certain discrete set of distances from the nucleus. ...
1
vote
0answers
21 views

Spontaneous parametric down conversion and relative time of emission of two entangled photons

A pump beam excites a non-linear crystal which produces two entangled photons with perpendicular polarization, namely in the state $|HV>+|VH>$. Are there examples where one of the photons was ...
3
votes
3answers
79 views

Why, in spin sums, we sum over final spin states and average over initial states?

I am reading Halzen's book about quarks and leptons and on page 120 he talks about spin sums. He says that in order to calculate the amplitude between unpolarized states we have to sum over FINAL ...
1
vote
2answers
84 views

Commuting operators and Direct product spaces

Under what conditions is the common eigenspace of two commuting hermitian operators isomorphic to the direct product of their individual eigenspaces? When can an eigenket $|\lambda$1$\lambda$2$>$ ...
2
votes
1answer
189 views

Evaluate $\langle \mathbf{p} | 1/\hat{r} | \mathbf{p}' \rangle$

In Sakurai's Problem 1.27 b), we use $\langle \mathbf{r} | \mathbf{p}\rangle = e^{i\mathbf{p}\cdot\mathbf{r}/\hbar}$ to show that $$ \langle \mathbf{p} | F(\hat{r}) | \mathbf{p}' \rangle = ...
4
votes
2answers
125 views

Does $\sigma_x\sigma_p = 0 \cdot \infty$ after a measurement of particle position?

I feel this question has an obvious answer that I should have been able to find independently, but I've searched for a while now it hasn't clicked. When position is measured, the uncertainty of the ...
2
votes
1answer
26 views

Reconciling electron subshell configurations and the Pauli exlcusion principle

I'd like to prefix this with an apology: I have no formal training in QP, and most of what I know has been obtained by reading Wikipedia. As such, it'd be really helpful if any answers took my lack of ...
1
vote
1answer
222 views

Non-trivial solution for a linear set of coefficients involved in the phonon modes of a semiconductor quantum dot

I am trying to use the method outlined in this linked paper (T. Takagahara, Journal of Luminescence, 70 (1996), pp. 129-143) to find the phonon-exciton coupling in a spherical PbS quantum dot. In Eq ...
1
vote
2answers
42 views

How does Dirac conclude that $X_r(c_r)$ cannot vanish?

On page 32 of Dirac's book Principles of Quantum Mechanics, he considers the case when the linear, Hermitian$^1$ operator $\xi$ satisfies an algebraic equation $$\phi(\xi)\equiv(\xi - c_1)(\xi - ...
4
votes
1answer
78 views

Evolution of harmonic oscillator in path integral formulation

The unnormalized ground state of the harmonic oscillator (choosing units such that $m = \hbar = \omega = 1)$ is $$\tag{1}\psi(q,t) = \exp(-q^2/2-it/2).$$ The transition function is ...
2
votes
1answer
44 views

How to prove that if the expectation value of $A$ in any state is real, then $A$ is Hermitian?

If the expectation value of operator $A$ in any state is real, then $A$ is Hermitian. there is an uncompleted proof: $$ \int(c_1\psi_1+c_2\psi_2)^* A (c_1\psi_1+c_2\psi_2)dx$$ ...