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Tagged with harmonic-oscillator hamiltonian
3 questions
32
votes
1
answer
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Evolution operator for time-dependent Hamiltonian
When I studied QM I'm only working with time independent Hamiltonians. In this case the unitary evolution operator has the form $$\hat{U}=e^{-\frac{i}{\hbar}Ht}$$ that follows from this equation
$$
i\...
- 1,034
7
votes
5
answers
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How can zero-point energy have any measurable effect when it is just a constant offset to the Hamiltonian?
In classical (say Hamiltonian) mechanics, adding a constant energy offset has no effect on the dynamics of the physical system. One way to understand this might be to understand that Hamilton's ...
- 15.2k
3
votes
1
answer
158
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Peskin and Schroeder, where is the mass in the denominator of the simple harmonic oscillator Hamiltonian?
This relates to page 20 of Peskin and Schroeder.
They state that the Fourier transform of the Klein-Gordon field satisfies the following:
$$\left[\frac{\partial^2}{\partial t^2}+(|\vec p|^2+m^2)\right]...
- 7,008