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noblegas
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Homework Statement
use the hamiltonian equation H=H_x+H_y+H_z to show that wave functions of the form
[tex]\varphi[/tex](r)=[tex]\phi[/tex]i(x)[tex]\phi[/tex]j(y)[tex]\phi[/tex]k(z)
where the functions phi_i(x) are the energy eigenfunctions for a 1-d SHM , satisfy H*phi=E*phi , and find the followed values of E for the 3-d oscillator
Homework Equations
H=-h-bar^2/2m*del^2+1/2*K*r^2, k is a constantr^2=x^2+y^2+z^2
del^2=d^2/dx^2+d^2/dy^2+d^2/dz^2
The Attempt at a Solution
H=d^2/dx^2(-h-bar^2/2m)+1/2*k*x^2+
Homework Statement
use the hamiltonian equation H=H_x+H_y+H_z to show that wave functions of the form
[tex]\varphi[/tex](r)=[tex]\phi[/tex][SUBi[/SUB](x)[tex]\phi[/tex]j(y)[tex]\phi[/tex]k(z)
where the functions phi_i(x) are the energy eigenfunctions for a 1-d SHM , satisfy H*phi=E*phi , and find the followed values of E for the 3-d oscillator
Homework Equations
H=-h-bar^2/2m*del^2+1/2*K*r^2, k is a constantr^2=x^2+y^2+z^2
del^2=d^2/dx^2+d^2/dy^2+d^2/dz^2
The Attempt at a Solution
H=d^2/dx^2(-h-bar^2/2m)+1/2*k*x^2+
Homework Statement
use the hamiltonian equation H=H_x+H_y+H_z to show that wave functions of the form
[tex]\varphi[/tex](r)=[tex]\phi[/tex][SUBi[/SUB](x)[tex]\phi[/tex]j(y)[tex]\phi[/tex]k(z)
where the functions phi_i(x) are the energy eigenfunctions for a 1-d SHM , satisfy H*phi=E*phi , and find the followed values of E for the 3-d oscillator
Homework Equations
H=-h-bar^2/2m*del^2+1/2*K*r^2, k is a constantr^2=x^2+y^2+z^2
del^2=d^2/dx^2+d^2/dy^2+d^2/dz^2
The Attempt at a Solution
H=d^2/dx^2(-h-bar^2/2m)+1/2*k*x^2+d^2/dy^2(-h-bar^2/2m)+1/2*k*y^2+d^2/dz^2*(h-bar^2/2m)+1/2*k*z^2
not sure how to proceed with my solution but I am sure the equation i*h-bar*dphi/dt=H*ohi will play a role in helping me form my final solution