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Questions and Answers
What is the Hamiltonian operator of the harmonic oscillator in one dimension?
What is the Hamiltonian operator of the harmonic oscillator in one dimension?
- Ĥ = p̂2 - mω 2 x̂2 / 2m
- Ĥ = p̂2 1 + mω 2 x̂2 / 2m (correct)
- Ĥ = p̂2 - mω 2 x̂2 * 2m
- Ĥ = p̂2 + mω 2 x̂2 / 2m
What does the eigenvalue equation for the harmonic oscillator look like in the {|xi} representation?
What does the eigenvalue equation for the harmonic oscillator look like in the {|xi} representation?
- − ~2 d2ϕ(x)/dx2 + mωxϕ(x) = Eϕ(x) (correct)
- ~2 d2ϕ(x)/dx2 − mωxϕ(x) = Eϕ(x)
- ~2 dϕ(x)/dx + mωxϕ(x) = Eϕ(x)
- ~2 d3ϕ(x)/dx3 + mωxϕ(x) = Eϕ(x)
What can be deduced about the eigenvalues of the Hamiltonian from the form of the potential function?
What can be deduced about the eigenvalues of the Hamiltonian from the form of the potential function?
- The eigenvalues of the Hamiltonian are positive. (correct)
- The eigenvalues of the Hamiltonian are zero.
- The eigenvalues of the Hamiltonian are negative.
- The eigenvalues of the Hamiltonian are complex.
What happens to the eigenvalues E of the Hamiltonian if the potential function V (x) is greater than its minimum value Vm?
What happens to the eigenvalues E of the Hamiltonian if the potential function V (x) is greater than its minimum value Vm?
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What kind of system is described by the Hamiltonian operator for the harmonic oscillator?
What kind of system is described by the Hamiltonian operator for the harmonic oscillator?
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