05_04_04 - 116 Projection amplitudes and ket vectors for...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
[email protected] 116 04/04/2005 Projection amplitudes and ket vectors for free states - = Ψ = Ψ x x x e x x x all 1 all 2 2 2 σ π - - - = Ψ k k e k all 1 2 2 2 1 2 2 all all x ik x x ik k e x k x x k k e k x k k x x - = Ψ = Ψ = Ψ = Ψ Gaussian probability distribution at t=0: 2 2 2 1 ) 0 , ( x e x - = Ψ Satisfies the requirements for projection amplitudes: And is a stationary state of the free Schrödinger equation: * x k k x = k x x k = Φ ) ( m k k k x m E x E x 2 2 2 2 2 2 2 ), ( ) ( = Φ = Φ - While these stationary basis states cannot be normalized to 1, any wave function is normalized to 1. Ψ
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
[email protected] 117 04/04/2005 The uncertainty principle and ground-state energies x Area in which the ground state wave function has to be confined Momentum uncertainty in all three dimensions x x p 1 2 2 2 2 3 0 ) ( x m E Example: Hydrogen atom 2 2 2 4 1 2 0 4 0 1 8 0 ) ( 0 0 0
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/28/2008 for the course PHYS 316 taught by Professor Hoffstaetter during the Spring '05 term at Cornell University (Engineering School).

Page1 / 5

05_04_04 - 116 Projection amplitudes and ket vectors for...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online