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I.What to recall about motion in a central potential II.Example and solution of the radial equation for a particle trapped within radius “a” III.The spherical.

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Presentation on theme: "I.What to recall about motion in a central potential II.Example and solution of the radial equation for a particle trapped within radius “a” III.The spherical."— Presentation transcript:

1 I.What to recall about motion in a central potential II.Example and solution of the radial equation for a particle trapped within radius “a” III.The spherical square well (Re-)Read Chapter 12 Section 12.3 and

2 Ignore center of mass motion Focus on this “H μ ” m1m1 m2m2 O 2

3 the angular momentum operator 3

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6 6 Normalization not yet specified Spherical Neuman function, r=0, so get D=0

7 7 I.Particle in 3-D spherical well (continued) II.Energies of a particle in a finite spherical well Read Chapter 13

8 8 In spectroscopy the rows are labelled by:

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10 10 I. Energies of a particle in a finite spherical square well

11 11 V(r) a 0 -V 0 r I II 0

12 12 V(r) a 0 -V 0 r I II 0 0 +V 0

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15 15 y 0π/2π3π/2 2π5π/2 3π7π/24π LHS(-cot)

16 16 y 0π/2π3π/2 2π5π/2 3π7π/24π How the value of λ affects the plot: y1y1 y2y2 y3y3

17 17 V(r) a 0 -V 0 r I II 0

18 18 To solve this define: and Then the radial equation becomes: The solution is:

19 19 I.Energies of a particle in a finite spherical square well, continued II.The Hydrogen Atom

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22 22 I.Energies of a particle in a finite spherical square well (continued) II.The Hydrogen Atom

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24 24 # protons in nucleus Charge of electron energy levels

25 25 Defined as E<0

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27 27 solution

28 28 I.The Hydrogen Atom (continued) II.Facts about the principal quantum number n III.The wavefunction of an e - in hydrogen

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34 34 I.Facts about the principal quantum number n (continued) II.The wavefunction of an e - in hydrogen III.Probability current for an e - in hydrogen

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37 37 Normalization not determined yet

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39 39 I.Facts about Ψ e in hydrogen II.Probability current for an e - in hydrogen Read 2 handouts Read Chapter 14

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41 41 E>0 (scattering) states (we will study these in Chapter 23) E<0 (bound) states

42 42 etc. 2p 2s 3p 3s The n=1 shell The n=2 shell The n=3 shell

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44 44 Review Syllabus Read Goswami section 13.3 and chapter 14 plus the preceding chapter as necessary for reference

45 45 Read Chapter 14 I.Probability current for an e - in hydrogen II.The effect of an EM field on the eigen functions and eigen values of a charged particle III.The Hamiltonian for the combined system of a charged particle in a general EM field

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48 48 A O

49 49 angular momentum operator magnetic momentum operator quantum number “m” This factor is called the Bohr magneton Magnitude of the z- component of magnetic dipole moment of the e -

50 50 I.The effect of an EM field on the eigen functions and eigen values of a charged particle II.The Hamiltonian for the combined system of a charged particle in a general EM field III.The Hamiltonian for a charged particle in a uniform, static B field Read Chapter 15

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52 52 I.The Hamiltonian for a charged particle in an EM field II.The Hamiltonian for a charged particle in a uniform, static B field III.The normal Zeeman effect

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57 57 O

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66 66 Set = 0 for now H 2D, HO

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