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Results tagged with quantum-mechanics
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user 10606
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.
1
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2
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231
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Diagonalization of this Hamiltonian: How do I transform the differential operators?
In order to find the eigenstates of this Hamilatonian
$$
H = \sum_{j=1}^3 \left( - \frac{\hbar^2}{2m} \frac{\partial^2}{\partial x_j^2}\right)
+ \frac{1}{2} m \omega^2 \left( (x_1 - x_2)^2 + (x_1 - x …
- 632
1
vote
2
answers
355
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Mnemonic for creation and anhiliation operators [closed]
I am not sure if this is question is withing the scope of this page. I have an exam in quantum mechanics in a few weeks and I always confuse anhilation and creation operator.
$$
a^\dagger |n\rangle = …
- 632
1
vote
1
answer
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Eigenvalues of the Spin Operator on a two-spin-system
I am not sure if I understand spin operators correctly. Given a two spin system in state $|++\rangle$ and an operator $S = S^{(1)} + S^{(2)}$
Then I have
$$
S_z |++\rangle
= (S^{(1)}_z + S^{(2)}_z) …
- 632
4
votes
3
answers
10k
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Commutator of $L^2$ and $X^2$, $P^2$
In our quantum mechanics script, it states that $[L^2, X^2] = 0$ and $[L^2, P^2] = 0$, therefore for the following Hamiltonan
$$H = \frac{P^2}{2m} + V(X^2)$$
it is that $[H, L^2] = 0$ therefore $H$ …
- 632
5
votes
2
answers
8k
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Second-order energies of a quartic pertubation of a harmonic oscillator [closed]
A homework exercise was to calculate the second-order perturbation of a quantum anharmonic oscillator with the potential
$$
V(x) = \frac{1}{2}x^2 + \lambda x^4.
$$
We set $\hbar = 1$, $m=1$, etc. Usin …
- 632