DOC PREVIEW
CALTECH APH 161 - Lecture notes

This preview shows page 1-2 out of 7 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 7 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 7 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 7 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

SJ_QMnotesSJ_QMnotes0001SJ_QMNotesp20001.pdfMB_QMnotes.pdfPlan of action: - Background; - “Postulates” of QM; - Application #1: Particle in a Box Application #2: Atomic orbitals; Hints leading to QM: - Discrete spectral lines; - Specific heats of solids (Law of Dulong and Petit, 3R); - Photoelectric effect; - Davisson-Gerner experiment (electron diffraction); Theoretical Responses: - Discrete spectral lines: Niels Bohr →22422126.13nhmeeVnEnπ−=−=; - De Broglie: “pilot waves” Attribute a wavelength to matter: ph=λ; Classical Mechanics Quantum Mechanics 1) The “state” of a system { }iipq, “wave function” )(xψ 2) Evolution Equations iiqHp∂∂−=; iipHq∂∂= ψψHtiˆ=∂∂ 3) Observables and measurements Any mechanical variable we might be interested in is a function of p’s and q’s, e.g. 22212kqmpE += i) ≡dxx2)(ψprobability that particle will be found between x and x+dx ii) “Expected” value of an observable, Cˆ, is given by CxCˆ)(ˆ*ψψψψ∫= Question: What observables? In QM, observables are represented by “operators” 3D: ∇−=ip; 1D: dxdipx−= Particle in a box: Schrödinger equation:ψψψExVdxdm=+− )(2222 V(x) = 0 by rearranging: 02222=+ψψmEdxd → xmEBxmEA222sin2cos+=ψ Boundary conditions: ψ(0)= ψ(na)=0 → ditch cosine πnamE=22 → 22222manEnπ= Toy model of molecular binding: 222""222maEatomsπ×= 222)(22amEmoleculeαπ×= −=−⋅=2222222222221222ααππαπmamaamEbond


View Full Document

CALTECH APH 161 - Lecture notes

Documents in this Course
Lecture 2

Lecture 2

12 pages

Lecture 3

Lecture 3

18 pages

Load more
Download Lecture notes
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Lecture notes and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Lecture notes 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?