5 Quantum Mechanics

The total energy of a particle (e.g., an electron in an atom, a free electron, an electron in an electric field, a conduction electron in a solid) is the sum of the

V m

p E

Vpv

VmvE







potential and kinetic energies. Expressed in terms of momentum p, and mass m, this is stated:



mvp since

 

  





 

 

hfE

h

k

f

Considering movement in one dimension only,

let

t iE

x ip

  





i2 = 1 Now, the potential energy, V, may depend upon the position and time, and so in general, V = V(x,t).