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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 onedimensional 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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 Spring '09
 Anlage
 Physics, Energy, Work, Perturbation theory, secondorder perturbation theory

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