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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32 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: ...
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1answer
135 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 ...
2
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1answer
81 views

Simple systems whose classical and quantum Hamiltonians differ

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
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2answers
331 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
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2answers
75 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
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1answer
120 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
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2answers
90 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 ...
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1answer
37 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 ...
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1answer
110 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
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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 ...
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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 $$ \langle x | H | n \rangle = E_n \langle x | n \rangle \tag{2} $$ ...
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2answers
102 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 ...
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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 ...
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0answers
84 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 $t>t'$. ...
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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.
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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}] = [ ...
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1answer
34 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 ...
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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 ...
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2answers
122 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 ...
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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
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81 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 ...
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1answer
56 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 ...
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476 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. ...
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0answers
20 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
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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 ...
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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
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1answer
168 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
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2answers
124 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
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1answer
25 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
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1answer
217 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 ...
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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
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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
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1answer
42 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: $$ \int(c_1\psi_1+c_2\psi_2)^* A (c_1\psi_1+c_2\psi_2)dx$$ ...
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1answer
102 views

What is the difference between the Bohr model of the atom and Schrödinger's model?

What is the difference between the Bohr model of the atom and The solution of the Schrödinger equation for the hydrogen atom? Are there any difference between definition of the electric potential ...
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19 views

Schrodinger equation with unknown potential function [duplicate]

How to find wave function if potential function is unknown. I have only the scattering data: time and coordinates of scattering particle.
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3answers
92 views

Is the ground state closest to the uncertainty relation? [duplicate]

For simplicity, suppose we are only talking about discrete energy levels, ie, bound state case. The energy levels are $E_1, E_2\cdots$, and the corresponding wave functions are $\psi_1, \psi_2 ...
9
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1answer
139 views

Why Lorentz group for fields and Poincaré group for particles?

Wigner treatment associates to particles the irreps of the universal covering of the Poincaré group $$\mathbb{R}(1,3)\rtimes SL(2,\mathbb{C}).$$ Why don't we consider finite dimensional ...
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31 views

Beta plus decay…explain one thing [duplicate]

Can anyone please explain how, in beta plus decay, a nucleon can gain mass by changing from a proton to a neutron? Where does it get the extra mass from? Does it convert energy in some way? Does ...
2
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0answers
57 views

“Good” States In Degenerate Perturbation Theory

During the section on Degenerate Perturbation Theory, Griffiths (Introduction to Quantum Mechanics 2ed) starts with a general linear combination of two orthogonal eigenfunctions of $H_0$. He walks ...
2
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1answer
27 views

Simple Mach-Zehnder Interferometer with Polarizing Beam Splitters

I am wondering which state leaves the simple interferometer below. The beam splitters are polarizing beam splitters (PBS) which transmit vertical polarization and reflect horizontal polarization. Say ...
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2answers
52 views

Double Slit Experiment with a slanted slit

If you consider the dark spots on the pattern produced by the double slit experiment to maybe be a shadow of the slitless area of the dividing wall between and around the slits, as silly a thought as ...
2
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2answers
47 views

quantum mechanics operators - Hermitian or complex conjugate?

Let $f(x)$ be a normalised state in a 1-D system. Let $g(x) = iA f(x)$, where $A$ is a Hermitian operator. I want to find the inner product of $g(x)$ with itself. Is it $$\int \left(-i A^\dagger ...
4
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2answers
64 views

Tensors of rotations about an arbitrary vector in C^2

I'm trying to solve the following equation: $$e^{-i\theta/2 \sigma_{\vec{i}}^A} \otimes e^{-i\theta/2 \sigma_{\vec{i}}^B} |\Psi\rangle_{AB} = e^{i\phi} |\Psi\rangle_{AB} $$ where $e^{i\phi}$ should ...
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2answers
85 views

System without ground state is not real in nature?

We know that Coulomb force is real phenomena in nature and with Coulomb potential $V(x) \thicksim -\frac{1}{|x|}$ lowest energy is bounded in hydrogen atom. But it's mathematically clear that if ...
1
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1answer
68 views

Interpretation of $\vec{x}$ in QFT

I am still at an early stage of studying Quantum Field Theory (I am reading QFT In A Nutshell by A. Zee). In the book I'm reading, it starts from a discrete lattice of material "lumps" labeled by ...
3
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60 views

Density matrix formalism and group representation

The postulates of quantum theory can be given in the density matrix formalism. States correspond to positive trace class operators with trace 1 on a Hilbert space $\mathcal{H}$. Composition is defined ...
1
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1answer
137 views

Complex Quantum Wave [closed]

Can the complex nature of quantum wave arise from the fact that particle is represented as wave packet in spatial frequency and particle's total energy is represented as wave packet in time frequency? ...
1
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1answer
94 views

How does Dirac form this conjugate imaginary equation?

On page 30 of Dirac's book $$\xi|P\rangle = a|P\rangle\tag{12}$$ He then says Suppose we have a solution of (12) and we form the conjugate imaginary equation, which will read $$\langle ...
3
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1answer
44 views

What is relationship between Quantum tunnelling and Gravitational potential energy of stars?

Are there a direct mathematical relationship between Quantum tunnelling and Gravitational potential energy of stars? The true source of the Sun's energy was shown by Hans Bethe to be nuclear fusion ...
2
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2answers
40 views

Observing a particle over a certain domain

I was just thinking: in Quantum Mechanics, we start out with that whole collapsing business by observing the x position of a particle. I was thinking: why do we have to do that? What if we only ...