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Quantum Mechanics

by: Marjorie Hahn

Quantum Mechanics PHYSICS 137A

Marjorie Hahn

GPA 3.95

M. Crommie

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M. Crommie
Class Notes
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This 1 page Class Notes was uploaded by Marjorie Hahn on Thursday October 22, 2015. The Class Notes belongs to PHYSICS 137A at University of California - Berkeley taught by M. Crommie in Fall. Since its upload, it has received 18 views. For similar materials see /class/226690/physics-137a-university-of-california-berkeley in Physics 2 at University of California - Berkeley.

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Date Created: 10/22/15
4 Postulates of Quantum Mechanics 1 Every physically realizable state of a particle can be described by a state vector or quotwavefunctionquot 1 that can be represented as a vector in the Hilbert space of all possible linearly independent states 2 Observable quantities such as energy momentum position and angular momentum are represented by Hermitian operators that act on the state function 1 If Q is the operator representing the observable quotqquot then the observable fq is represented by the operator fQ If you measure the observable quotqquot for a particle then you are certain to get an eigenvalue 7 of Q In the position representation the momentum operator is p hiddX 3 If a measurement of Q is made on a particle described by 1 then the probability of getting the particular eigenvalue 7 is equal to the magnitude squared of the overlap of 1 onto fl Here f is the eigenfunction of Q associated with 7 If the measurement actually results in 7 then the wavefunction of the particle collapses from 1 to f 4 The time development of a state function 1 t is determined by the time dependent Schroedinger Eq n ihddt 1 t H 1 t where H is the Hamiltonian or energy operator


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