physics 451
Download
Skip this Video
Download Presentation
Physics 451

Loading in 2 Seconds...

play fullscreen
1 / 11

Physics 451 - PowerPoint PPT Presentation


  • 97 Views
  • Uploaded on

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Physics 451' - prisca


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
physics 451

Physics 451

Quantum mechanics I

Fall 2012

Oct 12, 2012

Karine Chesnel

slide2
Announcements

Homecoming

slide3
Quantum mechanics

Announcements

  • Homework next week:
  • HW # 13 due Tuesday Oct 16
  • Pb 3.3, 3.5, A18, A19, A23, A25
  • HW #14 due Thursday Oct 18
  • Pb 3.7, 3.9, 3.10, 3.11, A26
slide4
Infinite- dimensional space

Wave function are normalized:

Hilbert space: functions f(x) such as

Quantum mechanics

Hilbert space

N-dimensional space

Wave functions live in Hilbert space

slide5
Norm

Orthonormality

Schwarz inequality

Quantum mechanics

Hilbert space

Inner product

slide6
Expectation value

since

For any f and g functions

Observables are Hermitian operators

Examples:

Quantum mechanics

Hermitian operators

Observable - operator

slide7
Stationary states – determinate energy

Generalization of

Determinate state:

Standard deviation:

For determinate state:

operator

eigenstate

eigenvalue

Quantum mechanics

Determinate states

slide8
Quantum mechanics

Quiz 16

Since any wave function can be written as a linear combination

of determinate states (stationary states), for which we can write

The wave function is itself a determinate state and we can write

  • True
  • B. False
slide9
For a given transformation T, there are “special” vectors for which:

is transformed into a scalar multiple of itself

is an eigenvector of T

l is an eigenvalue of T

Quantum mechanics

Eigenvectors & eigenvalues

slide10
Find the N roots

Spectrum

Quantum mechanics

Eigenvectors & eigenvalues

To find the eigenvalues:

We get a Nth polynomial in l: characteristic equation

slide11
Hermitian operator:

Quantum mechanics

Hermitian transformations

1. The eigenvalues are real

2. The eigenvectors corresponding to distinct eigenvalues are orthogonal

3. The eigenvectors span the space

ad