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energy

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.

mason-hayden
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energy

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  1. 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 = -U0 classical forbidden region classical forbidden region position x

  2. U(x) Physically unacceptable solution: wavefunction diverges to +  E = 177.0 eV Physically acceptable solution: wavefunction converges to 0 E = 173.5 eV Physically unacceptable solution: wavefunction diverges to - E = 170.0 eV

  3. 1st excited state n = 2, E2 = -296.63 eV ground state n = 1, E1 = -373.84 eV 2nd excited state n = 3, E3 = -173.5 eV 3nd excited state n = 4, E4 = -21 eV

  4. E = - 373.797386eV E = - 373.797396eV E = - 373.797300eV

  5. anti-nodal line – constructive interference slit 1 slit 2 nodal line – destructive interference

  6. U U = 0 x force on bound electron F F = 0 x x = 0

  7. 1 2 5 6 4 8 7 9 10

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