CHEM 4502 Lecture Notes - Lecture 6: Correspondence Principle, Momentum Operator, Beta-Carotene
Document Summary
Particle in tall box solved schrodinger eqn psi doesn"t tell where particle is . tells what energy is psi^ 2 tells where it is likely to be (probability density distribution) As n infinity, the distribution will look like a straight line equally likely to be everywhere as quantum number gets large, it becomes more classical. Correspondence principle: qm must agree w/ classical results in the limit of large n (quantum #) Now that we have the wavefunction, we can determine probability of finding particle in any region of box using. (x) ( x) dx x 2 x 1. 0 sin2( x a )dx= 2 a( x. X above = statistical definition need to go to qm definition. X dx x2 [ dx x ]2. Need to sandwich operator between conjugates of wave function. The avg position of particle given by sandwiching operator x btwn wavefunctions. X 2 a xsi n2( n x a )dx a.
