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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.

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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:

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2 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)

3 U(x)U(x) Physically acceptable solution: wavefunction converges to 0 E = eV Physically unacceptable solution: wavefunction diverges to +  E = eV Physically unacceptable solution: wavefunction diverges to -  E = eV

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

5 E = eVE = eVE = eV

6 nodal line – destructive interference anti-nodal line – constructive interference slit 1 slit 2

7 x x U U = 0 F = 0 x = 0 F force on bound electron

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