Q6:1 A two-dimensional harmonic oscillator has a quantum hamiltonian operator H given by 1 H = 2m dx² ™ dy² 2m (dz + ay) +mw² (z° + y*). Write down the time independent Schrödinger equation for this oscillator. (i) Show that the Schrödinger equation for this H can be written as two one-dimensional equations by explicit separation of variables.
Q6:1 A two-dimensional harmonic oscillator has a quantum hamiltonian operator H given by 1 H = 2m dx² ™ dy² 2m (dz + ay) +mw² (z° + y*). Write down the time independent Schrödinger equation for this oscillator. (i) Show that the Schrödinger equation for this H can be written as two one-dimensional equations by explicit separation of variables.
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![Q6:1 A two-dimensional harmonic oscillator has a quantum hamiltonian operator H given by
1
2m (ər* Əye) +mw² (x² + y²).
Write down the time independent Schrödinger equation for this oscillator.
(i) Show that the Schrödinger equation for this H can be written as two one-dimensional equations
by explicit separation of variables.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff258f736-2efe-4abc-a546-b1bd73d984a7%2F5c63e3da-a7a3-4796-b463-2cadf198816e%2Fgugn6f8_processed.png&w=3840&q=75)
Transcribed Image Text:Q6:1 A two-dimensional harmonic oscillator has a quantum hamiltonian operator H given by
1
2m (ər* Əye) +mw² (x² + y²).
Write down the time independent Schrödinger equation for this oscillator.
(i) Show that the Schrödinger equation for this H can be written as two one-dimensional equations
by explicit separation of variables.
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