# energy position x U(x)U(x) U = 0 E U = -U 0 E = K + U E < U  K < 0 E > U  K > 0 classical forbidden region classical forbidden region classical allowed.

## Presentation on theme: "energy position x U(x)U(x) U = 0 E U = -U 0 E = K + U E < U  K < 0 E > U  K > 0 classical forbidden region classical forbidden region classical allowed."— Presentation transcript:

energy position x U(x)U(x) U = 0 E U = -U 0 E = K + U E < U  K < 0 E > U  K > 0 classical forbidden region classical forbidden region classical allowed region positive curvature positive curvature negative curvature U(x)U(x)

U(x)U(x) 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

ground state n = 1, E 1 = -373.84 eV 1 st excited state n = 2, E 2 = -296.63 eV 2 nd excited state n = 3, E 3 = -173.5 eV 3 nd excited state n = 4, E 4 = -21 eV

E = - 373.797300 eVE = - 373.797386 eVE = - 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

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