Physics Problems 298

Physics Problems 298 - 294 Chapt 39 Photons and Matter...

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 294 Chapt. 39 Photons and Matter Waves b) Given that ψ ∗ ψ dv = 1 (i.e., ψ is normalized), show that i 2 where |ai | = |ai |2 = 1 , a∗ ai . i c) The time-independent Schr¨dinger equation for our system can be written o Hφi = Ei φi , where H is called the Hamiltonian operator or just HAMILTONIAN. For one dimensional systems −2 ∂ 2 h H=− + V (x) . 2m ∂x2 The Hamiltonian acting on the eigenfunction φi changes it into itself times Ei . Note Ei is just a CONSTANT NUMBER and can be taken out of any integral. Now it turns out that the mean energy Emean of a system with H and wave function ψ has a value given by Emean = ψ ∗ Hψ dv . Show that Emean = i |ai |2 Ei also. For no good reason mean values in quantum mechanics are called expection values. So Emean is the expectation value of the Hamiltonian. 039 qfull 03000 3 5 0 tough thinking: Einstein, Runyon 6. “God does not play dice”—Einstein. Discuss. ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online