null
US
Sign In
Sign Up for Free
Sign Up
We have detected that Javascript is not enabled in your browser. The dynamic nature of our site means that Javascript must be enabled to function properly. Please read our
terms and conditions
for more information.
Next up
Copy and Edit
You need to log in to complete this action!
Register for Free
709292
Quantum Mechanics
Description
Mind Map on Quantum Mechanics, created by franz.sciortino on 02/04/2014.
Mind Map by
franz.sciortino
, updated more than 1 year ago
More
Less
Created by
franz.sciortino
over 10 years ago
119
0
0
Resource summary
Quantum Mechanics
Finite Square Well, potential step and barrier
Simple Harmonic Oscillator (SHM)
Five postulates of QM
post.2 --> Properties of Hermitian operators
post.1 --> wavefunctions of dynamical variables
post.3 --> x and p operators, others for dynamical variables (as classically)
post.4 --> prob. densities by sum of expansion coefficients (squared)
post. 5 --> time dependence as by TDSE
Wavefunction collapses by interferences with the system
Commutators (Herm.) vs. anticommutators (anti-Herm.)
Compatibility of observables --> common set of eigenstates (e.g. H and p for free particle)
If Q & R commute and have unique eigenvalues, then are compatible
Dirac notation: see summary table in lect.10 notes
Expectation values and uncertaity
<Q>=sum((a_n)^2 *q_n) or <Q>= int(psi* Q psi)
Ehrenfest Theorem: eq. of motion for expectation values of observables follow classical counterparts
RMS spread: Delta(q)= int(mod(Q psi)^2) or <Q^2>-<Q>^2
HUP: apply Schwartz inequality to difference operators (e.g. Q') with commutators and anticommutators;
Find that <[Q', R']> = <[Q,R]>
Consider only imaginary part, with [x,p] included, for the HUP statement
Continuous eigenvalues: swap Kronecker with Dirac delta + integration rather than summation (see notes lect.14)
Continuous eigenstates cannot be normalised - mostly multiply by a Gaussian factor to get wavepackets
Show full summary
Hide full summary
Want to create your own
Mind Maps
for
free
with GoConqr?
Learn more
.
Similar
Quantum Mechanics
emmalmillar
Chem 1B Midterm 2 Review (UCSC- Active Learning)
Faylenn McDonough
5.1 Section
Denisse Guajardo
PHYS2041 Quantum Mechanics
Lucy Lowe
QM4
jake1923
Schroedinger Equation
Domhnall Murphy
CLASS 11 CHEMISTRY: STRUCTURE OF ATOM
KungFu_Pawn ezhuvath
Untitled
dimuthuo
Area, Volume & Perimeter Mind Map
rory.examtime
AS AQA Geography- Rivers
Hannah Goodenough
AS Sociology - Education Theories
HannahLB
Browse Library