Lecture 12: 02/13/09
II1,3 Plausibility Argument leading to Schrödinger's Equa tion:
II1,4 Physical Significance of the Wave Function ΨΨΨΨ(x,t):
A. 0
B. 1
C. infinite
D. Something else
( )∫∞
∞−
=Ψ ?, 2dxtxFor a proper wave function,
0 1 2 3 4 5-1.5
-1
-0.5
0
0.5
1
1.5am
plitu
de
x [arb. units]
real(Ψ)imag(Ψ)
ΨΨ*
0 0.2 0.4 0.6 0.8 1-2
-1
0
1
2
ampl
itude
x [arb. units]
real(Ψ)imag(Ψ)
ΨΨ*
II1,5 Expectation Values
A. x=0
B. Something between –L/2 and +L/2
C. Something between – ∞∞∞∞ and +∞∞∞∞D. Something else
A particle is associated with the following wave function:
for –L/2<x<L/2
elsewhere
If the position x of the particle would be measured, the result would be:
( ) tieLx
Ltx ωπ −=Ψ )cos(
2,
( ) 0, =Ψ tx
A. <x> = 0
B. <x> = L/2
C. <x> = -L/2
D. <x> ≈≈≈≈ L/4
E. Something else
A particle is associated with the following wave function:
for –L/2<x<L/2
elsewhere
What is the expectation value of the position < x>?
( ) tieLx
Ltx ωπ −=Ψ )cos(
2,
( ) 0, =Ψ tx
Symmetry of probability density about x=0! -> <x> =0