Summary of 1st lecture classical physics explanation of black-body radiation failed (ultraviolet catastrophe) Planck’s ad-hoc assumption of “energy quanta” of energy Equantum = h, leads to a radiation spectrum which agrees with experiment. old generally accepted principle of “natura non facit saltus” violated Other evidence for “quantization”: Photoelectric effect (Einstein: explained by “photon” hypothesis) Atomic spectra stability of atom Quantum theory born as attempt to address these observations 2 Outline Recap Steps toward QM ...
C Nave @ gsu.edu http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Outline • Postulates of QM • Picking Information Out of Wavefunctions – Expectation Values – Eigenfunctions & Eigenvalues • Where do we get wavefunctions from? – Non-Relativistic – Relativistic • What good-looking s look like • Techniques for solving the Schro Eqn – Analytically – Numerically – Creation-Annihilation Ops Postulates of Quantum Mechanics • The state of a physical system is completely described by a wavefunction . • All information ...
A wave function in quantum mechanics describes the quantum state of an isolated system of one or more particles. There is one wave function containing all the information about the entire system, not a separate wave function for each particle in the system. Wave equation for the harmonic motion 2 2 d (x) 2 (x) 2 dx 2 2 d (x) (x) 4 2 dx2 1 p2 E mv2 V V 2 2m 1 p [2mE V]2 h h p ...
Time-dependent Schrodinger Equation Without potential E = T With potential E = T + V Erwin Rudolf Josef Alexander Schrodinger Austrian 1887 –1961 Postulates of Quantum Mechanics Postulate 1: The state of a quantum mechanical system is completely specified by a wave function ψ (r,t) that depends on the coordinates of the particles (r) and time t. These functions are called wave functions or state functions. For 2 particle system: (x,y,z,x ,y ,z ,t) 1 ...
Postulates of Quantum Mechanics (from “quantum mechanics” by Claude Cohen-Tannoudji) nd Q 2 postulate: Every measurable physical quantity is described by an operator ˆ This operator is an observable. Q. 3rd postulate: The only possible result of the measurement of a physical quantity Q is one of the eigenvalues € ˆ of the corresponding Q . € observable 4th postulate (non-degenerate): When the physical quantity Q € ψ is measured on a system in the normalized state the probability of ...
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