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Physics 451

Physics 451. Quantum mechanics I Fall 2012. Nov 2, 2012 Karine Chesnel. Phys 451. Announcements. Homework tonight: HW #16 Friday Nov 2 by 7pm. Homework next week: HW #17 Tuesday Nov 6 by 7pm HW #18 Thursday Nov 8 by 7pm. Radial part. Angular part. or. Phys 451.

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Physics 451

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  1. Physics 451 Quantum mechanics I Fall 2012 Nov 2, 2012 Karine Chesnel

  2. Phys 451 Announcements • Homework tonight: • HW #16 Friday Nov 2 by 7pm • Homework next week: • HW #17 Tuesday Nov 6 by 7pm • HW #18 Thursday Nov 8 by 7pm

  3. Radial part Angular part or Phys 451 Normalization z r y x

  4. Angular part Pb 4.6 Phys 451 Orthonormality z r Spherical harmonics are orthogonal y x Also

  5. z r y x The angular equation The radial equation Phys 451 Schrödinger equation in spherical coordinates

  6. Change of variables Form identical to Schrödinger equation with an effective potential Centrifugal term Phys 451 The radial equation z r y x

  7. Inside the well Change of variables Phys 451 The radial equation V=0 Example: infinite spherical well

  8. For l = 0 solution Boundary condition Three quantum numbers: (n, l, m) here Phys 451 The radial equation V=0 Infinite spherical well

  9. solution Spherical Bessel function Spherical Neumann function Physical condition at r =0 Phys 451 The radial equation V=0 Infinite spherical well • If l≠ 0

  10. Phys 451 The radial equation V=0 Infinite spherical well • If l≠ 0 Physical condition at r = a :

  11. Phys 451 Quiz 22 When a particle is subject to a potential that depends on the radius only, which quantum numbers apply to quantize the energy? A. Only the principal quantum number n B. Only the azimuthal quantum number l C. Only the magnetic quantum number m D. Possibly both numbers (n,l) E. Possibly all three numbers (n,l,m)

  12. Pb 4.7: construct and Pb 4.8: case of l = 1 show that V=-V0 Pb 4.9: Finite spherical well Find the ground state (l =0) Phys 451 V=0 Spherical well show that they blow up at zero

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