energy
DESCRIPTION
E = K + U. U ( x ). U ( x ). U = 0. negative curvature. classical allowed region. positive curvature. energy. E > U K > 0. positive curvature. E. E < U K < 0. E < U K < 0. U = -U 0. classical forbidden region. classical forbidden region. - PowerPoint PPT PresentationTRANSCRIPT
ener
gy
position x
U(x)U = 0
E
U = -U0
E = K + U
E < U K < 0 E < U K < 0
E > U K > 0
classical forbidden region
classical forbidden region
classicalallowed region
2
2. .
dcurvature K E
dx
( )x
0 positive curvature
positive curvature
negative curvature
U(x)
U(x)
0 Physically acceptable solution:wavefunction converges to 0 E = 173.5 eV
Physically unacceptable solution:wavefunction diverges to + E = 177.0 eV
Physically unacceptable solution:
wavefunction diverges to - E = 170.0 eV
( )x
ground state n = 1, E1 = -373.84 eV 1st excited state n = 2, E2 = -296.63 eV
2nd excited state n = 3, E3 = -173.5 eV 3nd excited state n = 4, E4 = -21 eV
E = - 373.797300 eV E = - 373.797386 eV E = - 373.797396 eV
nodal line – destructive interference
anti-nodal line – constructive interference
slit 1
slit 2
x
x
U
U = 0
F = 0
x = 0
F
force on bound electron
dUF
dx
-1.5 -1 -0.5 0 0.5 1 1.5
x 10-10
-400
-350
-300
-250
-200
-150
-100
-50
0Potential Well: SQUARE
x (nm)
ener
gy
(eV
)
-1.5 -1 -0.5 0 0.5 1 1.5
x 10-10
-400
-350
-300
-250
-200
-150
-100
-50
0Potential Well: STEPPED
x (nm)
ener
gy
(eV
)
-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2-400
-350
-300
-250
-200
-150
-100
-50
0
50
100Potential Well: DOUBLE
x (nm)
ener
gy
(eV
)
-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15-400
-350
-300
-250
-200
-150
-100
-50
0Potential Well: SLOPING
x (nm)
ener
gy
(eV
)
-3 -2 -1 0 1 2 3
x 10-10
-35
-30
-25
-20
-15
-10
-5
0Potential Well: Truncated PARABOLIC
x (nm)
ener
gy
(eV
)
-1 0 1 2
x 10-10
-5
0
5
10
15
20
25Potential Well: MORSE potential
x (nm)
ener
gy
(eV
)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-350
-300
-250
-200
-150
-100
-50
0Potential Well: Lattice
x (nm)
energ
y
(eV
)
1 2
4 5 6
7 8 9 10