Classically, we can think of matter as masses connected by tiny springs. a) In quantum theory, how is this classical mod
Posted: Thu May 12, 2022 11:50 am
- Classically We Can Think Of Matter As Masses Connected By Tiny Springs A In Quantum Theory How Is This Classical Mod 1 (131.94 KiB) Viewed 28 times
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approximate Hamiltonian and the nergies of low-lying states for
atoms of mass, M, in the given potential."
Classically, we can think of matter as masses connected by tiny springs. a) In quantum theory, how is this classical model qualitatively vindicated as a simple harmonic oscillator? Assume an arbitrary potential function has a stable equilibrium point at x=X and the displacements of the atoms from equilibrium are small, then expand the potential around the equilibrium point. a 12 b) Given the potential function V = V. ) = : ()" -(0)"} Hamiltonian and the r r energies of low-lying states for atoms of mass, M, in the given potential. The quantity V. is positive and has the dimensions of energy. To keep it simple, assume that the system is 1-D. Let x be the displacement from equilibrium.
- - Harmonic Oscillator 1 v.(E)= n , 2" n! = 1 H. (Ele 5/2 1/4 ะป Ho = = - 2 II = 24 H, = 482 โ 2 Hz = 853 โ 12 II = 1644 - 4862 +12 3 - 4 no E. =(-) =n7 "= k W= ั