1. For each of the following systems below, identify the zero order Hamiltonian (H) and first...
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1. For each of the following systems below, identify the zero order Hamiltonian (H) and first order perturbation (H), and write out the general expression for solving for the first-order correction to the energy of state n, E,(¹). a. A harmonic oscillator with the potential U(x) = d 3 kx² + x³ + x² 20 b. A particle constrained to a 1D box 0 ≤ x ≤a with the potential U(x) = 0 for 0 ≤ x ≤ a/2 and U(x) = b * e for a/2 ≤x≤ a 4TE c. A hydrogen atom placed in an external electric field, e. The Hamiltonian operator of this system is H = ² + er • E. 2μ (Note: er is the instantaneous dipole moment of an electron. Hint: The dot product of two vectors is: A. B = |A|B|cose) 1. For each of the following systems below, identify the zero order Hamiltonian (H) and first order perturbation (H), and write out the general expression for solving for the first-order correction to the energy of state n, E,(¹). a. A harmonic oscillator with the potential U(x) = d 3 kx² + x³ + x² 20 b. A particle constrained to a 1D box 0 ≤ x ≤a with the potential U(x) = 0 for 0 ≤ x ≤ a/2 and U(x) = b * e for a/2 ≤x≤ a 4TE c. A hydrogen atom placed in an external electric field, e. The Hamiltonian operator of this system is H = ² + er • E. 2μ (Note: er is the instantaneous dipole moment of an electron. Hint: The dot product of two vectors is: A. B = |A|B|cose)
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