Download presentation

Presentation is loading. Please wait.

1
Wave mechanics in potentials Modern Ch.4, Physical Systems, 30.Jan.2003 EJZ Particle in a Box (Jason Russell), Prob.12 Overview of finite potentials Harmonic Oscillator (Don Verbeke), Prob.48 Hydrogen atom

2
Infinite Square well: V(0<x<L) = 0, V= outside

3
Overview of finite potentials Finite well: can spill out Tunneling through finite barriers

4
Harmonic oscillator: V(x) =1/2 kx 2

5
Hydrogen atom : Bohr model We found r n = n 2 r 1, E n = E 1 /n 2, where the “principle quantum number” n labels the allowed energy levels. Discrete orbits match observed energy spectrum

6
Hydrogen atom: Orbits are not discrete (notice different r scales)

7
Hydrogen atom: Schrödinger solutions depend on new angular momentum quantum numbers Quantization of angular momentum direction for l=2 Magnetic field splits l level in (2l+1) values of m l = 0, ±1, ± 2, … ± l

8
Hydrogen atom examples from Giancoli

12
Summary: You can calculate permitted states and energies from boundary conditions Finite wells and barriers need reflection/transmission analysis Infinite square well has E n ~n 2 E 1 Harmonic oscillator has evenly spaced E Hydrogen atom: 3D spherical solution to Schrödinger equation yields 3 new quantum numbers: l = orbital quantum number m l = magnetic quantum number m s = spin = ±1/2

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google