量子力學導論 Textbook Introduction to Quantum Mechanics / David J. Griffiths

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Presentation transcript:

量子力學導論 Textbook Introduction to Quantum Mechanics / David J. Griffiths Prentice Hall / 1995 Reference Principles of Quantum Mechanics - as applied to chemistry and chemical physics Donald D. Fitts Cambridge University Press / 1999

量子力學導論 Chap 1 - The Wave Function Chap 2 - The Time-independent Schrödinger Equation Chap 3 - Formalism in Hilbert Space Chap 4 - 表象理論

Chap 1 - The Wave Function Quantum Mechanics Chap 1 - The Wave Function ► Schrödinger equation Classical mechanics: Newton’s second law : wave function time-depedent Schröinger equation :

Quantum Mechanics ► Statistical interpretation Born’s statistical interpretation : { probability of finding the particle between x and (x+dx) at time t } ► Probability is probability density The probability of infinite interval :

Quantum Mechanics ► Normalization (i) If is a solution , then is also a solution. Normalized the wave function to determine the factor A (ii) If the integral is infinite for some wave functions, no factor to make it been normalizable. The non-normalizable wave function cannot represent particles. (iii) the condition of wave function which can be normalizable

Quantum Mechanics ► Operator and expectation value (average / mean) expectation value of position x : expectation value of momentum : operator x represent position; operator represent momentum in x-direction. ■ all physics quantities can be written in terms of position and momentum

Quantum Mechanics ► Heisenberg uncertainty principle (proof ref. chap 3) standard deviation the variance of distribution, where individual physics quantity

Quantum Mechanics so standard deviation in position standard deviation in momentum