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Flashcards in QM - Exact solutions to the SE Deck (8)
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1

Describe and state examples of a harmonic oscillator

  • A pendulum
  • Vibrating spring

 

A harmonic oscillator occurs when a system experiences a restoring force proportional to the displacement from eqilibrium 

2

Draw a one-dimensional harmonic oscillator and derive the Hamiltonian

3

Describe the total energy E

 

E is constant as it is an eigenvalue. As it is constant it must be independent from x

4

State how to transform cartesian coordinates into spherical coordinates

5

Draw the first four wavefunctions for a harmonic oscillator and their associated probabilities

6

Describe the eigenvalue of the ground state 

E0 =/= 0 is called thr zero point energy. It is not equal to zero as molecules are always vibrating

7

Revise particle in a box!

8