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Curvature and Energy Relations in Quantum Physics

Explore the classical allowed and forbidden regions, positive and negative curvature implications on energy levels. Understand physically acceptable vs. unacceptable solutions in quantum mechanics.

mason-hayden
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Curvature and Energy Relations in Quantum Physics

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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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