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by: Ashley Kunze


Ashley Kunze
GPA 3.61

M. Bowers

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M. Bowers
Class Notes
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Popular in Chemistry and Biochemistry

This 3 page Class Notes was uploaded by Ashley Kunze on Thursday October 22, 2015. The Class Notes belongs to CHEM 113B at University of California Santa Barbara taught by M. Bowers in Fall. Since its upload, it has received 80 views. For similar materials see /class/226936/chem-113b-university-of-california-santa-barbara in Chemistry and Biochemistry at University of California Santa Barbara.




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Date Created: 10/22/15
Postulates of 5 Quantum Mechanics I The wave function I belonging to a system of n particles is a function of x1 y1 Z1xn yn zn and t Comments Since particles have wavelike properties it is reasonable that their motion is described by a wave function 11 The wave equation for I is obtained from the classical expression for the total energy of the system by replacing the dynamical variables by operators Dmamical Variable Operator x position a x linear momentum h a a px 139 x it 6 W t tal 0 energy a i at and by inserting I as the operand Comments Following the postulate for a single particle in one dimension W kinetic energy potential energy 2 W lmvj Vx PX 2 2m Vx 39 substituting for px and W h 0 hi 02 P t 7 V k t I at x E 2m 0x2 06 x This is the wave equation for a single particle in one dimension 0 Often called the Schrodinger equation 0 Solutions depend on the potential energy Vx 0 Similar equations follow for more particles in more dimensions Summary of Definitions A Symmetry Elements 1 Re ections 0 6 V contains the principal rotation axis usually the Z axis Oz 0 4 I d 6d contains the principal rotation axis and Vi r 2 bisects the angle between two C2 axes that ll are J to the principal axis 0 d C4 Z 1 TA X 6h perpendicular to the prmc1pal rotation axis 0 h ie in the xy plane 2 Inversion i re ects all atoms orbitals through a center of symmetry Rotations 2739E a CD rotation axis with a n symmetry b The principal rotation axis has the largest value of n lmEroEer Rotations Sn Cn 6h 0r 0h Cn where neither CD or 6h is a symmetry element on its own 0h Principal Point Groups Cn CnV Cnh Dn Dnh Dnd Td contains contains contains contains contains contains contains E CD CD2 CDT E Cn Chm 1 nGV or nGd E CD i andor Oh and S s E CD nC2JCn E CD i and or 6h nC2JCn sometimes S 6V 6d E CD nC2JCn nGd S2n sometimes I E C3 C2 54 Cd


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