Lecture 15 - Quantum mechanics

Lecture 15 - Quantum mechanics - Observing the electron...

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Unformatted text preview: Observing the electron with light disturbs its movement between slit and detector. x h p = mv h = Heisenberg Uncertainty Principle Position of Baseball vs. Electron = p = p Schrodinger Wave Equation Bohr theory of H-atom fails to explain emission spectra of larger atoms. Bohr model violates Heisenberg uncertainty principle (defined e- orbits). Bohr model ignores wave properties of the electron. Schrdinger Wave Equation : Total energy (E) is sum of potential energy (V) and kinetic energy (T) r e z 2 2 4 2 2 mv e- + r E V T = + 1,2,3,... n n 2 = = r ) sin( ) , ( t x k A t x n n n + t) (x, E t) (x, V dx t) (x, d m 8 h n 2 n 2 2 2 n n = + Solutions are called stationary state wave functions ( (x) ) or bound states (i.e. standing waves that do not change with time) Time-independent Schrdinger Equation ) ( ) ( x E x H n n n = V dx d m h H + = 2 2 2 8 Probability Distribution dx x ) ( 2 = Hamiltonian (Total Energy) KE PE (x) E (x) V dx (x) d m 8 2 2 2 = + h Quantum Mechanical Wave Function Properties of Wave functions ( ( x ) ): (x) is mathematical description of the wave properties. (x) does NOT have any physical meaning by itself. 2 ( x ) dx gives probability of particle between x and x+dx. (1) (x) must have a single value at every point x. (2) (x) must be finite at any point. (3) (x) must be continuous and first derivative also continuous. Probability between x 1 & x 2 = 2 1 2 ) ( x x dx x Unacceptable Wave Functions Not single valued! Not continuous Derivative not continuous Particle in a One-dimensional Box L x V L x < < = V = V L x or x Particle located inside the box if V = 0: e- E V dx d m 8 h 2 2 2 2 = + E * dx d m 8 h 2 2 2 2 = + Translational motion (V=0) Solution to Particle in a Box...
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This note was uploaded on 04/06/2011 for the course CHEM 107B taught by Professor Jamesames during the Winter '09 term at UC Davis.

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Lecture 15 - Quantum mechanics - Observing the electron...

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