(McQuarrie 5-30) The Hamiltonian for a 3-D harmonic oscillator is given by, მ2 + მ2 + V(x, y, z) 2u \ მ2 მყ2 Əz² ħ2 მ2 Ĥ + where the potential energy is: 1 1 V (x, y, z) == ½ k²x² + ½ kyy² + 1½ k₂ z² 글++ Use separation of variables to argue that that the wave functions are given by: Vnx,ny,nz (x, y, z) = Vnz (x) Vny (y) Vnz (2) where the (u) are the 1-D harmonic oscillator wave functions (u= x, y, or z) and that the energies are: Enz,ny,nz = = hvx (nx = ( n + 1 ) + hvy (ny + 1 ) + hvz (m² + ½ ) nz ku for v₁ = 1½ (k) 1/2 μ

(McQuarrie 5-30) The Hamiltonian for a 3-D harmonic oscillator is given by, მ2 + მ2 + V(x, y, z) 2u \ მ2 მყ2 Əz² ħ2 მ2 Ĥ + where the potential energy is: 1 1 V (x, y, z) == ½ k²x² + ½ kyy² + 1½ k₂ z² 글++ Use separation of variables to argue that that the wave functions are given by: Vnx,ny,nz (x, y, z) = Vnz (x) Vny (y) Vnz (2) where the (u) are the 1-D harmonic oscillator wave functions (u= x, y, or z) and that the energies are: Enz,ny,nz = = hvx (nx = ( n + 1 ) + hvy (ny + 1 ) + hvz (m² + ½ ) nz ku for v₁ = 1½ (k) 1/2 μ

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter11: Quantum Mechanics: Model Systems And The Hydrogen Atom

Section: Chapter Questions

Problem 11.61E: What is the physical explanation of the difference between a particle having the 3-D rotational...

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