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Results tagged with quantum-mechanics
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user 364663
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 quantum-field-theory tag for the theory of many-body quantum-mechanical systems.
5
votes
Accepted
Physical interpretation of selection rules for different multipole orders
One way to understand dipole or multipole fields are through the multipolar expansion. The idea is simple: Consider that you have a distribution of charges in space. Of course it produces some potenti …
- 3,237
1
vote
Exchange interactions between Spins in Ising model
I know of three-body or many-body interactions that are consequence of an effective description of the dynamics of one system, given some conditions. I'll sketch some argument about how it appears.
W …
- 3,237
3
votes
Possible errata Landau and Lifshitz in $\S29$ Matrix elements of vectors in Quantum Mechanic...
I don't know what is wrong with your reasoning, since it seems to return the right result in the special case where $A_{yy}=A_{zz}$. That said, I never saw this approach, and I searched in Landau'book …
- 3,237
0
votes
Proof of nodes of bound states using the wronskian
First, I want to make sure of something. The fact that the wronskian is zero doesn't imply that the wavefucntions are linearly dependant. actually, if the wavefucntions are linearly dependant,this im …
- 3,237
0
votes
What are the exact relations between bound states, discrete spectra, and negative energies i...
To shed light in this shadowed folk wisdom, let's stablish some facts.
The most general argument that I know, and you could find it in this wiki article is based on WKB approximation. The thing is th …
- 3,237
2
votes
How to prove this equation in quantum information theory?
If I understand it correctly, $\mathcal P_n$ forms a basis for Hermitian operators acting over the space of $n$ qubits. For example, if $n=1$, $\mathcal P_1 = \{\mathbb I,X,Y,Z\}$, and any state $\rho …
- 3,237
1
vote
How to Derive an Expression for First-Order Correction in Adiabatic Perturbation Theory?
Consider the time-dependent Schrodinger equation
$$
i\hbar |\dot\psi_m\rangle = H |\psi_m\rangle.
$$
If the state was an eigenvector of $H$, it would be easy to solve it. The solution would be somethi …
- 3,237
2
votes
Time-reversal without time translation symmetry
Time reversal operator is defined through a sequence of postulates, that generally includes
Its action on position operator $T\mathbf xT^\dagger = \mathbf x$
Its action on momentum $T\mathbf p T^\dag …
- 3,237
4
votes
1
answer
144
views
Is the Classical limit of Quantum theory the Newtonian Mechanics?
Recently I started to study Quantum Dissipative models like Caldeira-Leggett model and it occurs to me that this model provides a Quantum to Classical transition, but the Classical resultant system sa …
- 10.2k
0
votes
Arguing that the time derivative of $\exp(-iHt)$ is $-iH\exp(-iHt)$ without taylor expansion
But I cannot see how I can ignore the eigenvectors as if they do not exist and use chain rule
Do you want to prove it without using the spectrum or Taylor expansion?
Let $U(t) = e^{-iHt}$. By defini …
- 3,237
2
votes
Rabi Hamiltonian in the presence of a dc magnetic field
Consider first the Hamiltonian $H_0= \frac 12 \hbar \omega_0 \sigma_z$. The eigenvalues are $\pm \frac 12 \hbar \omega_0$ and the eigenvectors $|\uparrow:z\rangle,|\downarrow:z\rangle$. Now, before tu …
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5
votes
Accepted
Why do we say $E=hf$ supports particle nature of light?
which supports the particle nature of light.
In fact, it doesn't. First, Planck's law is not only about this mathematical relation, but it includes a discretization process.
The density of modes per …
- 3,237
9
votes
Angular orientation of exact solution of the Hydrogen Schrödinger Equation
We can find a nice visual representation of the Spherical Harmonics in this wiki article. You can see that in fact, only $l=0$ is spherically symmetric.
We know that:
The ground state is the only tr …
- 998
1
vote
Question about the Possibility of Measuring the Position of Particles in a Double-Slit Exper...
If it were possible to obtain information about the particle's position while maintaining the interference pattern created by the particle, I believe that, like in the Copenhagen interpretation, we c …
- 3,237
1
vote
Why the Fourier transform of dipole expectation value is proportional to the power?
Well, it's not my area so I have no idea how to show a rigorous formal proof of this relation. But I can give you what I think is more than a hand-waving argument. Something like a formal-hand rigorou …
- 3,237