![5. The Harmonic Oscillator Consider a general problem in 1D Particles tend to be near their minimum Taylor expand V(x) near its minimum Recall V'(x 0 ) - ppt download 5. The Harmonic Oscillator Consider a general problem in 1D Particles tend to be near their minimum Taylor expand V(x) near its minimum Recall V'(x 0 ) - ppt download](https://images.slideplayer.com/32/10073499/slides/slide_17.jpg)
5. The Harmonic Oscillator Consider a general problem in 1D Particles tend to be near their minimum Taylor expand V(x) near its minimum Recall V'(x 0 ) - ppt download
![SOLVED: As was proven in class, the basic commutation relation between the position and momentum operators is [x,p] = Use this and the operator identity for commutators of product operators (also proven SOLVED: As was proven in class, the basic commutation relation between the position and momentum operators is [x,p] = Use this and the operator identity for commutators of product operators (also proven](https://cdn.numerade.com/ask_images/1ebcef2e9ae049358ffcc28486d9aef0.jpg)
SOLVED: As was proven in class, the basic commutation relation between the position and momentum operators is [x,p] = Use this and the operator identity for commutators of product operators (also proven
![SOLVED: Given the operator position X =x; momentum p =-ih and the operator Hamiltonian H dx h? 0? H = +V 2m dr2 where V is a generic potential depending on .x, SOLVED: Given the operator position X =x; momentum p =-ih and the operator Hamiltonian H dx h? 0? H = +V 2m dr2 where V is a generic potential depending on .x,](https://cdn.numerade.com/ask_images/2aa74ab968ad4ac5bd4fbd7cad8ea6fb.jpg)
SOLVED: Given the operator position X =x; momentum p =-ih and the operator Hamiltonian H dx h? 0? H = +V 2m dr2 where V is a generic potential depending on .x,
![SOLVED: The Hamiltonian for the quantum mechanical harmonic oscillator is p? H =T+V = 2m m? 12 The momentum operator is given by ihV The commutator between two matrices A and B SOLVED: The Hamiltonian for the quantum mechanical harmonic oscillator is p? H =T+V = 2m m? 12 The momentum operator is given by ihV The commutator between two matrices A and B](https://cdn.numerade.com/ask_images/638eb34b74554a53a6fd97ed41039f3b.jpg)