assign01 - Physics 5110 Homework 1(due Jan 20 1 Sketch the...

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Physics 5110 Homework 1 (due Jan 20) January 12, 2010 1. Sketch the radial wave functions of the electron in the hydrogen atom for the 1S, 2S, and 2P orbitals. (Plot amplitude vs radius r . On the r axis, use units of the Bohr radius a 0 .) (See Tipler, Section 7-3). 2. A particle of mass m moves in a three-dimensional simple harmonic oscillator potential of the form V ( x, y, z ) = 1 / 2 k ( x 2 + y 2 + z 2 ) If you know how to solve the problem of a one-dimensional oscillator, then the three-dimensional oscillator is easy, since mathematically, it separates into three one-dimensional oscillators. The energy eigenstates are just a product of the eigenstates ψ n of the one-dimensional oscillator (Tipler, Section 6-6): ψ n x ,n y ,n z ( x, y, z ) = ψ n x ( x ) ψ n y ( y ) ψ n z ( z ) where we have separate quantum numbers for each of three directions ( n x , n y , n z ), and the corresponding energy is just the sum of the energies of the three independent oscillators E n x ,n y ,n z = ¯
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This note was uploaded on 07/12/2010 for the course PHYSICS 5010 taught by Professor Rosenthaal during the Spring '10 term at Utah.

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assign01 - Physics 5110 Homework 1(due Jan 20 1 Sketch the...

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