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 ...
Outline Introduction Problems of classical physics Black-body Radiation experimental observations Wien’s displacement law Stefan – Boltzmann law Rayleigh - Jeans Wien’s radiation law Planck’s radiation law photoelectric effect observation studies Einstein’s explanation Quantum mechanics Features postulates Summary Quantum Physics 2 Question: What do these have in common? lasers solar cells transistors computer chips CCDs in digital cameras Ipods superconductors ......... Answer: They ...
2.2 Postulates of Quantum Mechanics Quantum mechanics is the math framework for the development of physical theories The basic postulates below were derived after a long process of trial and (mostly) error The motivation for the postulates is not always clear and appear surprising even to experts 2.2.1 Postulate 1: State Space Associated to any isolated physical system is a Hilbert space ...
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 &bull ...
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 ...
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 ...
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 ...
Definition of Computational Chemistry • Computational Chemistry: Use mathematical approximations and computer programs to obtain results relative to chemical problems. • Computational Quantum Chemistry: Focuses specifically on equations and approximations derived from the postulates of quantum mechanics. Solve the Schrodinger equation for molecular systems. • Ab Initio Quantum Chemistry: Uses methods that do not include any empirical parameters or experimental data. What’s it Good ...
Schrodinger Equation We take Schrodinger’s equation as one of the postulates of quantum mechanics Schrodinger himself just “figured it out” Thus there is no formal proof We rely on comparison of its predictions with experiment to validate it But we’ll briefly try to motivate it 2 Schrodinger Equation We’d like the quantum wave equation To be consistent with de Broglie-Einstein relations ...
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