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Results tagged with time-evolution
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user 230943
The quantum mechanical time evolution operator governs how observables and/or states evolve during finite time steps, and is always unitary. Use this tag for questions about the time evolution operator, or the different equations of motion in the Schrödinger/Heisenberg/Dirac pictures. For time-independent Hamiltonians, the time evolution operator is simply exp(-iHt).
3
votes
1
answer
389
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Form of the interaction representation time evolution operator
I am a bit confused about the interaction representation picture. Consider the time independent Hamiltonian $H = H_0 + V$. My question concerns the interaction representation time evolution operator:
…
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0
votes
1
answer
143
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The Adiabatic Theorem and Symmetries of the Hamiltonian
For this question, all operators and states are on a finite dimensional Hilbert space.
Suppose I have a collection of continuously parametrized Hamiltonians $H(t), 0\leq t\leq T$. Suppose furthermore …
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7
votes
Accepted
Is this proof of Griffith's watertight?
He does not say that $\Psi(x, t)$ must be normalized; he says it must be normalizable, meaning that
$$\int_{-\infty}^{\infty} |\Psi(x, t)|^2\text{d}t < \infty.$$
It is easy to see why $\Psi(x, t)$ mus …
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9
votes
3
answers
2k
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Why is imaginary time evolution non-unitary?
If I have a Hamiltonian $H$, the corresponding time-evolution operator is $e^{-iHt}$. If one defines the evolution operator in imaginary time, one uses $e^{-H\tau}$, where $\tau = it$.
It is commonly …
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