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Results tagged with quantum-mechanics
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user 186136
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.
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3
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Harmonic oscillator position expectation value
I'm trying to get the expected value as a function of time for the position, of a harmonic oscillator hamiltonian and a state vector $|\psi\rangle=a|0\rangle+b|2\rangle$.
I have
$$|\psi(t)\rangle=ae^{ …
1
vote
1
answer
68
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Derivating operator acting on ket
I'm deducing a formula, and I used the "product rule" $\frac{\partial}{\partial t}(A|\phi>)=(\frac{\partial A}{\partial t})|\phi>+A\frac{\partial}{\partial t}|\phi>$.
I'm actually getting the result I …
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2
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Virial theorem hydrogen atom
I calculated $\langle T \rangle$ and $\langle V \rangle$ as a function of time of a given state of the hydrogen atom $|\psi\rangle=a|1,0,0\rangle+b|2,0,0\rangle$ and I found that
$$\langle V \rangle …
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0
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232
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Average pressure on a 3D box
I have a particle inside a box of dimensions $L_{x},L_{y},L_{z}$
the energies are given by $E=\frac{\hbar^2}{2m}\pi^2\sum_{i}\frac{n_{i}^2}{L_{i}^2}$
I calculated the force by $-\frac{\partial E}{\p …
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1
answer
296
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Momentum operator dot a vector
Why is $P \cdot A = A \cdot P -i\hbar\nabla \cdot A$? I was just replacing $P=-i\hbar\nabla $ so I didn't get the first term on the right side
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1
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Confusion of measuring two quantities on a quantum system
Let's say there are two observables corresponding to two operators A and B, and let's say my system is in a state Phi where with probability 1 if I measure A I get 3 (let's say 3 Joules), If I measur …
2
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1
answer
551
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Symmetric potential well different solutions
I have solved $H|\psi\rangle=E_{n}|\psi\rangle$ with $V(x)=0$ from $-a<x<a$ and $\infty$ otherwise.
If I propose a solution of the form $\psi(x)=A_{n}e^{ikx}+B_{n}e^{-ikx}$ I arrive to the solution
$$ …
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Symmetric potential well different solutions
Solutions coincide for n=odd and an extra minus sign (wavefunctions are the same up to a phase factor, in this case $e^{i\pi}$). For n=even the solution from the piecewise function is the same than th …
2
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1
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743
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Volume of state in phase space free particle
I have to how a quantum state of a free particle between 0 and a occupies an area of $h$ in the phase space.
What I did was to calculate $\Delta x \Delta p$ and show that it was of order $h$, but I d …