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Unformatted text preview: 1 Physics 316 Solution for quiz 2 Spring 2005 Cornell University I. EXERCISE 1 If you have a potential V ( x ) with V (- x ) = V ( x ) and an initial wave function Ψ( x, 0) which is not symmetric and not anti-symmetric around x = 0 . Explain why the probability distribution | Ψ( x,t ) | 2 has to be time dependent. Answer: The stationary states associated with symmetric potentials must all be either symmetric or antisymmetric. Therefore Ψ( x, 0) is not a stationary state, which means that | Ψ( x,t ) | 2 must be time dependent. II. EXERCISE 2 In the approximation that the force between two Cl atoms in Cl 2 increases linearly with the distance between them, the absorption frequencies of Cl 2 have a constant spacing, like the energy levels of a harmonic oscillator. When Δ ω 35 is that spacing for a Cl isotope with 17 protons and 18 neutrons, and Δ ω 36 is the frequency spacing for a Cl isotope with 17 protons and 19 neutrons, what is Δ ω 35 / Δ ω 36 ? Answer: The frequency spacing Δ ω is proportional to the difference between two neighboring energy levels Δ E = ¯ h Δ ω . For a harmonic oscillator Δ E = ¯ hω , where if m is the oscillator mass then ω ∝ m- 1 / 2 . The requested ratio is then Δ ω 35 / Δ ω 36 = p 36 / 35 , where we have approximated the proton and neutron masses to be equal.where we have approximated the proton and neutron masses to be equal....
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This note was uploaded on 09/28/2008 for the course PHYS 316 taught by Professor Hoffstaetter during the Spring '05 term at Cornell.
- Spring '05