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# Science and Computers I PHY 307

Syracuse

GPA 3.93

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This 14 page Class Notes was uploaded by Ms. Bryce Wisoky on Wednesday October 21, 2015. The Class Notes belongs to PHY 307 at Syracuse University taught by Staff in Fall. Since its upload, it has received 23 views. For similar materials see /class/225633/phy-307-syracuse-university in Physics 2 at Syracuse University.

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Date Created: 10/21/15

Lecll o Intro to Quantum Mechanics o Numerical solution of SchO dinger s equa tion Whywhen quantum o Newton s laws give a very accurate descrip tion of the behavior of everyday objectsmotions 0 But they fail miserably to describe atoms o This was a crisis for physics at turn of cen tury u Eg Laws of EM Newton s mechanics predicts atoms should be unstable Electrons classically have any energy but see only discrete energies Energy of electromagnetic waves in vac uum infinite Diffraction of electrons Photoelectric effect light waves like particles Resolution 0 Radical Took many physicists about 20 years to discover 0 Discovered twice Schrodinger Heisenberg 1926 o Arguably become the most well tested and accurate scientific theory Quantum elec trodynamics Basics Discard notion that microscopic objects like electrons can a well defined position veloc ity etc Not a practical issue but one of principle Instead think of them as being described by a wavefunction IJxt Like a usual wave in sense that electron is not localized like a classical particle But this is a probability wave J13t2 yields probability of finding particle at 13 t Dynamics replace Newton s laws simple ordinary differential equations by Schrodnger s equation partial differential equation 4 Allowed energies II Need ffooodx 2x 1 Probability Thus need to choose correct solution as a gt oo Inside will get oscillations Must smoothly match at boundary Requires that E be very carefully chosen In general discrete set of possible E s en ergy level quantization What happens Find only discrete set of E work So both wavefunction and E are output from cal culation E0 gt me Otherwise cannot match with large 1 asymptotics Particle cannot be stationary at minimum of potential Quan tum fluctuations even for zero tempera ture E increases with number of oscillations Find E using bisection algorithm 10 Summary In QM speak only of probabilities Throw out notion that particles have simultane ously well defined positions and momenta Heisenberg uncertainty principle 6513619 2 h Probabilities gotten by solving Schrodinger equation Can be solved using same algo rithm as used for Newton s equations For bound state problems find discrete spec trum of allowed energiesstates Many other things we haven t talked about scattering making quantum observations relativity many particles approximation meth ods operators connection to classical physics 11 Lecll o Intro to Quantum Mechanics o Numerical solution of SchO dinger s equa tion Whywhen quantum o Newton s laws give a very accurate descrip tion of the behavior of everyday objectsmotions 0 But they fail miserably to describe atoms o This was a crisis for physics at turn of cen tury u Eg Laws of EM Newton s mechanics predicts atoms should be unstable Electrons classically have any energy but see only discrete energies Energy of electromagnetic waves in vac uum infinite Diffraction of electrons Photoelectric effect light waves like particles Resolution 0 Radical Took many physicists about 20 years to discover 0 Discovered twice Schrodinger Heisenberg 1926 o Arguably become the most well tested and accurate scientific theory Quantum elec trodynamics Basics Discard notion that microscopic objects like electrons can a well defined position veloc ity etc Not a practical issue but one of principle Instead think of them as being described by a wavefunction IJxt Like a usual wave in sense that electron is not localized like a classical particle But this is a probability wave J13t2 yields probability of finding particle at 13 t Dynamics replace Newton s laws simple ordinary differential equations by Schrodnger s equation partial differential equation 4 Allowed energies II Need ffooodx 2x 1 Probability Thus need to choose correct solution as a gt oo Inside will get oscillations Must smoothly match at boundary Requires that E be very carefully chosen In general discrete set of possible E s en ergy level quantization What happens Find only discrete set of E work So both wavefunction and E are output from cal culation E0 gt me Otherwise cannot match with large 1 asymptotics Particle cannot be stationary at minimum of potential Quan tum fluctuations even for zero tempera ture E increases with number of oscillations Find E using bisection algorithm 10 Summary In QM speak only of probabilities Throw out notion that particles have simultane ously well defined positions and momenta Heisenberg uncertainty principle 6513619 2 h Probabilities gotten by solving Schrodinger equation Can be solved using same algo rithm as used for Newton s equations For bound state problems find discrete spec trum of allowed energiesstates Many other things we haven t talked about scattering making quantum observations relativity many particles approximation meth ods operators connection to classical physics 11

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