Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with quantum-mechanics
Search options not deleted
user 36793
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.
2
votes
2
answers
105
views
How do quantum numbers combine when two quantum systems combined?
Quantum numbers are sometimes additive (e.g., baryon number, lepton number, $3$-component of the angular momentum, etc), sometimes multiplicative (e.g., parity), and at times, neither additive nor mul …
- 27.2k
3
votes
Why is the ground state important in condensed matter physics?
The equilibrium properties at low-enough temperatures (for metals at room temperatures, $k_BT\ll E_F$ where $E_F$ is the Fermi energy) can be determined by knowing the properties of the ground state.
…
- 27.2k
2
votes
2
answers
120
views
The definition of the weaker notion of symmetry in the sense of Wigner's theorem
The weaker notion of symmetry, in the sense of Wigner's theorem, is a transformation on the states that leave all quantum mechanical amplitudes invariant. This tells that such transformations are repr …
- 27.2k
4
votes
2
answers
661
views
In what sense is a quantum damped harmonic oscillator dissipative?
The classical Hamiltonian of a damped harmonic oscillator $$H=\frac{p^2}{2m}e^{-\gamma t}+\frac{1}{2}m\omega^2e^{\gamma t}x^2,~(\gamma>0)\tag{1}$$ when promoted to quantum version, remains hermitian. …
- 27.2k
4
votes
2
answers
2k
views
Understanding real and complexified Lie algebras of ${\rm SO(3)}$
In the form, $$[J_i,J_j]=i\epsilon_{ijk}J_k\tag{1}$$ the Lie algebra of ${\rm SO(3)}$, denoted by $\mathfrak{so}(3)$, is called real Lie algebra.
By taking complex linear combinations $J_{\pm}=J_1\pm …
- 27.2k
3
votes
2
answers
485
views
Why don't the oscillator coherent states disperse in time?
A Gaussian wavepacket is made of a continuum of frequencies (or energies) and stretches in time due to the phenomenon of dispersion: the different plane wave components with different frequencies trav …
- 27.2k
0
votes
2
answers
513
views
Symmetries of a differential equation, its solutions and hydrogen atom
A symmetry of a differential equation need not be shared by its solutions. However, under that symmetry, the one solution goes to another. For example, consider the time-independent Schrodinger equati …
- 27.2k
2
votes
1
answer
457
views
Classical angular momentum components are numbers. Can they be generators of some symmetry g...
In Quantum Mechanics (QM), angular momentum turn out to be the generator of rotational symmetry. This is trivial to see because in QM, angular momenta are defined by the commutation relations $$[J_j,J …
- 27.2k
0
votes
1
answer
285
views
Why should the $\phi^4$ term necessarily cause scattering while a $x^4$ term in anharmonic o...
Consider an anharmonic oscillator in quantum mechanics, described by the Hamiltonian $$H=\frac{p^2}{2m}+\frac{1}{2}m\omega^2x^2+bx^4.$$ The $bx^4$ term doesn't cause scattering. The effect of this ter …
- 27.2k
2
votes
1
answer
581
views
How is it possible to take the inner product of states which belong to two different Hilbert...
Question 1 In case of spontaneous breakdown of a continuous symmetry e.g. the ${\rm U(1)}$ symmetry, two different vacua can be labelled as $|\theta\rangle$ and $|\theta^\prime\rangle$, and they belon …
- 27.2k
0
votes
3
answers
140
views
How to see that $[\textbf{p}^2,\textbf{L}^2]=[\textbf{p}^4,\textbf{L}^2]=0$ without doing an...
The Hamiltonian of a particle moving under the influence of a central potential $V(r)$ given by $$H=\frac{\textbf{p}^2}{2m}+V(r)$$ commutes with $\textbf{L}^2\equiv L_x^2+L_y^2+L_z^2$. Without doing a …
- 27.2k
1
vote
4
answers
234
views
What is the electric field due to a coherent radiation? Is it polarized?
What is the time-structure (i.e., how does the magnitude and direction change with time) of the expectation value of the electric field $\langle\textbf{E}\rangle(t)$ of a radiation field described by …
- 27.2k
1
vote
1
answer
73
views
Result of the measurement of operators $A$ and $B$ on same state $|\psi\rangle$ if $[A,B]=0$
Consider a 3-dimensional Hilbert space spanned by the normalized eigenstates $|1\rangle,|2\rangle,|3\rangle$ of an operator $A$. Consider a normalized superposition, $|\psi\rangle=c_1|1\rangle+c_2|2\r …
- 27.2k
0
votes
1
answer
334
views
Particle trapped in a double well potential and "slowly" increasing the height of the potent...
Today I was musing over the following problem. Consider a non-relativistic particle confined in an one-dimensional double well potential of the form $V(x)=\kappa(x^2-a^2)^2$ where both $a$ and $\kappa …
- 27.2k
8
votes
2
answers
1k
views
Are identical particles always entangled even when not interacting?
Aren't the states of two identical particles always entangled even if they are not interacting? The states of two identical particles are either symmetric or antisymmetric i.e., cannot be written as p …
- 27.2k