Phys 402 Discussion 3

# Phys 402 Discussion 3 - this problem b Calculate the change...

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Phys 402 Spring 2009 Homework 3 Due Friday, February 20, 2009 @ 9 AM 1. Griffiths, 2 nd Edition, Problem 6.1 First-order perturbation theory with a delta-function in an infinite square well. Eigen-energy and ground state eigenfunction. 2. Griffiths, 2 nd Edition, Problem 6.4 (a) only Second-order perturbation theory for the above. Trick: Try writing 2 2 1 m n as m n B m n A + + to help sum the infinite series. 3. Griffiths, 2 nd Edition, Problem 6.5 (a) only Second-order perturbation theory for the charged harmonic oscillator in an electric field. 4. Griffiths, 2 nd Edition, Problem 6.11 Fine Structure constant Extra Credit #4 Degenerate Perturbation Theory Stark Effect in Hydrogen. In 1913 Stark observed a splitting of the Hydrogen Balmer series lines by applying an electric field E = 100,000 V/cm. a) Write down the perturbing Hamiltonian H’ for the electron. Neglect spin in

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Unformatted text preview: this problem. b) Calculate the change in energy of the ground state of Hydrogen to first order. c) Consider the n=2 states of Hydrogen. Find the new energies to first order. d) Calculate the new n=2 eigenfunctions. e) Roughly calculate the resulting splitting of the Balmer series H α line in an electric field of 100,000 V/cm. Physics 402 Spring 2009 Prof. Anlage Discussion Worksheet for February 18, 2009 1. Consider the one-dimensional anharmonic oscillator with Hamiltonian 4 x K H H ′ + = and the unperturbed Hamiltonian . 2 / ) 2 / ( 2 2 x k m p H x + = a) Write down an expression for the first order correction to the eigenenergies. b) Evaluate the expression for the first order correction to the eigenenergy of the n th harmonic oscillator state. Hint: Look back at Eqs. [2.69] and [2.66]. Physics GRE Quantum Mechanics!...
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Phys 402 Discussion 3 - this problem b Calculate the change...

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