This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 1 2 The Schrödinger Equation in 3D Central Potentials Angular Momentum Summary 3 The symbol means differentiate the function f with respect to x only while treating the remaining variables as constants. Similarly for y and z . Example: 4 The timeindependent Schrödinger equation in 3 dimensions is V( x,y,z ) is the potential energy function and the wave function Ψ ( x,y,z ) is, in general, a function of all 3 coordinates. E is the energy associated with the state described by the wave function 5 The 3D Schrödinger equation can be solved for a quantum object confined to a box with impenetrable walls by a wave function of the form L 3 L 1 L 2 Since the walls are assumed to be impenetrable, the wave function must go to zero at the walls. Why? 6 The boundary conditions on the walls implies k i L i = n i p , where i = 1, 2, 3 and n i = 1, 2,…, which implies the energy levels L 3 L 1 L 2 E n 1 n 2 n 3 = h 2 8 m n 1 2 L 1 2 + n 2 2 L 2 2 + n 3 2 L 3 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ which, for a cubical box, is E n 1 n 2 n 3 = h 2 8 mL 2 n 1 2 + n 2 2 + n 3 2 ( ) 7 Note that the quantum numbers n 1 n 2 n 3 = 211, 121, 112...
View
Full Document
 Spring '10
 PROSPER
 Angular Momentum, Schrodinger Equation, Atomic orbital

Click to edit the document details