Consider a one-dimensional anharmonic oscillator for which the potential function is V(x)=1/2kx?+ ax*: a. Write the full Hamiltonian for this oscillator. b. What system would serve as the most reasonable zero-order approximation for this oscillator in order to use perturbation theory most efficiently and effectively? c. Identify the zero and first order perturbation terms in your Hamiltonian. d. What is the zero order energy of the ground state for this oscillator? e. Write the integral and compute the first order correction to this energy.

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10.
Consider a one-dimensional anharmonic oscillator for which the potential function
is V(x)=1/2kx?+ ax*:
a. Write the full Hamiltonian for this oscillator.
b. What system would serve as the most reasonable zero-order approximation for this oscillator in order
to use perturbation theory most efficiently and effectively?
c. Identify the zero and first order perturbation terms in your Hamiltonian.
d. What is the zero order energy of the ground state for this oscillator?
e. Write the integral and compute the first order correction to this
energy.
Transcribed Image Text:10. Consider a one-dimensional anharmonic oscillator for which the potential function is V(x)=1/2kx?+ ax*: a. Write the full Hamiltonian for this oscillator. b. What system would serve as the most reasonable zero-order approximation for this oscillator in order to use perturbation theory most efficiently and effectively? c. Identify the zero and first order perturbation terms in your Hamiltonian. d. What is the zero order energy of the ground state for this oscillator? e. Write the integral and compute the first order correction to this energy.
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