Quantum mechanics I Fall 2012 Physics 451 Quantum mechanics I Fall 2012 Karine Chesnel

Monday Sep 3: NO CLASS (Holiday) Phys 451 Announcements Monday Sep 3: NO CLASS (Holiday) Homework 1: Today Aug 31st by 7pm Pb 1.1, 1.2, 1.3 Homework 2: Group presentations Sep 5th Homework 3: F Sep 7th by 7pm Pb 1.4, 1.5, 1.7, 1.8 Homework Help sessions: T Th 3-6pm

Famous scientist who contributed to the foundation Phys 451 Announcements Next class Sep 5th Group presentations Will count as homework 2, 20 points plus 5 quiz points for presenting Famous scientist who contributed to the foundation of Quantum Mechanics Einstein Schrödinger Planck De Broglie Heisenberg Dirac Pauli Born Bohr

Probabilities Quantum mechanics Discrete variables Examples of discrete distributions: Age pyramid for a certain population (Utah, 2000) Distribution of scores in a class

Probabilities Quantum mechanics Discrete variables Example: number of siblings for each student in the class Distribution of the system Probability for a given j: Average value of j: Average value of a function of j Average value “Expectation” value

Quiz 2a What is the definition of the variance? A. B. C. D. E. Quantum mechanics Quiz 2a What is the definition of the variance? A. B. C. D. E.

Probabilities Quantum mechanics Discrete variables The deviation: Variance The standard deviation

Distribution of scores Quantum mechanics Probabilities Discrete variables The variance defines how wide/narrow a distribution is Spectral analysis of a photograph brightness intensity Narrow: small s Wide: large s Distribution of scores in a class

Probabilities Quantum mechanics Continuous variables The probability of finding the particle in the segment dx The density of probability: Probability to find the particle between positions a and b: Normalization:

Probabilities Quantum mechanics Continuous variables Average values: Variance:

Connection to Wave function Quantum mechanics Connection to Wave function Density of probability (now function of space and time): Normalization: Solutions have to be normalizable: - needs to be square-integrable

Quiz 2b Is this wave function square integrable or not? A. YES B. NO Quantum mechanics Quiz 2b Is this wave function square integrable or not? A. YES B. NO

Can Y stay normalized in time? Quantum mechanics Normalization of Wave function Normalization: Can Y stay normalized in time? If Y satisfies the Schrödinger equation and is normalizable, then indeed