Chapter1_10 - PHY4604 R D Field Expectation Values and...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
PHY4604 R. D. Field Department of Physics Chapter1_10.doc University of Florida Expectation Values and Differential Operators (1) One Space Dimension: To make things easier we will start with just one spatial dimension x so that dx t x dx t x 2 ) , ( ) , ( Ψ = ρ is the probability of finding the particle at time t between x and x+dx and Ψ Ψ = Ψ = 2 1 2 1 ) , ( ) , ( ) , ( ) , , ( * 2 2 1 x x x x dx t x t x dx t x t x x P is the probability of finding the particle at time t between x 1 and x 2 ( i.e. x 1 x x 2 ). The average value of x is called the “expectation value” of x and is given by Ψ Ψ = >= < dx t x x t x dx t x x x ) , ( ) , ( ) , ( * Dynamical Quantities: What about momentum and energy? The average momentum (“expectation value” of p x ) is Ψ Ψ >= < dx t x p t x p x x ) , ( ) , ( * How do we proceed? Classically x = x(t) and p x = mdx/dt . Schrödinger’s Equation:
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Ask a homework question - tutors are online