-2 -1 0 1 2

x 10-10

-100

0

100Wavefunction: Stream of non-interacting particles

x ( m )

psi

(

m-0

.5 )

-2 -1 0 1 2

x 10-10

0

1

2

x ( m )

pha

se (

rad

)

-2 -1 0 1 2

x 10-10

0

5

10

x 1010

J (

s-1

)

x ( m )

realimag

constant probability current density for free particles

wavelength: phase cycles through 2

ener

gy

E

U = 0

U = U0

x = 0 +x

I

RT