8

CHAPTER 1. GENERAL ASPECTS

The HAMILTONian is

ˆ

~2

4+U (~r)

(1.4)

H =

2m

where U (~r) is the (Trap)potential. The solutions

jn :

ˆ

(1.5)

Hjn = en jn

are orthogonal and the set of functions jn (~r) is complete

Z

dr jn (r)jn0(r) = dnn0

(1.6)

å

j (~r)j

n

(~r

0) = d(~r

~r 0):

(1.7)

n

n

If the particle is free, i.e. U = 0 then n ! p and

jp = ei~p ~r

ep =

p2

:

(1.8)

2m