Chapter06 Quantum Mechanics II General Bibliography 1) Various wikipedia, as specified 2) Thornton-Rex, Modern Physics for Scientists & Eng, as indicated

Postulates of Quantum Mechanics All information that can be known about a particle/system is contained within the wavefunction  (x,t) The probability of finding the particle at (x,t) is given by   . – in a region  x about (x,t) by    x The probability of finding the particle anywhere is 100% or 1.

Postulates of Quantum Mechanics Every observable quantity is associated with an “Operator” which is used to extract the information from the wavefunction The expectation value (aka average) of an observable quantity is given by The time evolution of the wavefunction is determined by H = Hamiltonian

Example Functions Can it be a solution to the time-dependent Schroedinger Eqn?

Properties of Good Wavefunctions  must be finite everywhere  must be single-valued  and d   /dx must be continuous for finite well- behaved potentials V(x)  must be normalizable (generally   0 as x  inf)

Infinite Square Well

6.4 Finite Square Well

6.5 3-D Finite Square Well

6.6 Simple Harmonic Oscillator

For E tot less than barrier height