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1、Quantum Mechenics II,Ru-Keng Su 2005.1.5,Chapter 1 Foundation of Quantum Mechanics,1.1 State vector, wave function and superposition of states,This chapter evolves from an attempt of a brief review over the basic ideas and formulae in undergraduate-level quantum mechanics. The details of this chapte
2、r can be found in the usual references of quantum mechanics,1.1 State vector, wave function and superposition of states,1.1 State vector, wave function and superposition of states,1.1 State vector, wave function and superposition of states,1.2 Schrdinger equation and its solutions,1.2 Schrdinger equ
3、ation and its solutions,1.2 Schrdinger equation and its solutions,1D Schrdinger equation Infinite potential well,1.2 Schrdinger equation and its solutions,Infinite potential well,1.2 Schrdinger equation and its solutions,Harmonic oscillator,1.2 Schrdinger equation and its solutions,Harmonic oscillat
4、or,1.2 Schrdinger equation and its solutions,Harmonic oscillator,1.2 Schrdinger equation and its solutions,Harmonic oscillator,1.2 Schrdinger equation and its solutions,Harmonic oscillator,1.2 Schrdinger equation and its solutions,3D Schrodinger equation Central potential,1.2 Schrdinger equation and
5、 its solutions,Central potential,1.2 Schrdinger equation and its solutions,Coulomb potential,1.2 Schrdinger equation and its solutions,Coulomb potential,1.3 Operators,According to the Born statistical interpretation, The probability of finding a particle at position r is just the square of its wave
6、function,1.3 Operators,1.3 Operators,1.3 Operators,1.3 Operators,pi-ih/2i Cartesian rectangular coordinates 1st convention: pure coordinate partpure momentum part 2nd convention: mixed part,1.3 Operators,1.3 Operators,Commutator,1.3 Operators,Commutator,1.3 Operators,Commutator,1.3 Operators,Hermiti
7、an operator,1.3 Operators,Eigenequation,1.3 Operators,O - representation,1.3 Operators,O - representation,1.4 Approximation method,Perturbation independent of time Non -degenerate,1.4 Approximation method,Non -degenerate,1.4 Approximation method,Non -degenerate,1.4 Approximation method,Degenerate,1.
8、4 Approximation method,Degenerate,1.4 Approximation method,Advantages of this choice are,1.4 Approximation method,Degeneracy may be removed,1.4 Approximation method,Perturbation depending on time Key: How to calculate the transition amplitude,1.4 Approximation method,Perturbation depending on time,1
9、.4 Approximation method,Perturbation depending on time,1.4 Approximation method,Variational method Key: How to choose the trial wave function,1.4 Approximation method,Variational method,1.5 WKB method (Wentzel-Kramers-Brillouin),Basic idea: (Q.M.)(C.M) when h0 WKB Semi- Classical method: To find an
10、expansion of h and solve stationary Schrdinger equation,1.5 WKB method (Wentzel-Kramers-Brillouin),1.5 WKB method (Wentzel-Kramers-Brillouin),1.5 WKB method (Wentzel-Kramers-Brillouin),For 1D case,1.5 WKB method (Wentzel-Kramers-Brillouin),For 1D case,1.5 WKB method (Wentzel-Kramers-Brillouin),For 1
11、D case,1.5 WKB method (Wentzel-Kramers-Brillouin),Three regions: E U(x),1.5 WKB method (Wentzel-Kramers-Brillouin),Conservation of the probability,1.5 WKB method (Wentzel-Kramers-Brillouin),E = U(x) Turning points: The semi-classical approximation is not applicable,1.5 WKB method (Wentzel-Kramers-Br
12、illouin),E = U(x),1.5 WKB method (Wentzel-Kramers-Brillouin),E = U(x),1.5 WKB method (Wentzel-Kramers-Brillouin),E U(x),1.5 WKB method (Wentzel-Kramers-Brillouin),Example I:,1.5 WKB method (Wentzel-Kramers-Brillouin),E U(x),1.5 WKB method (Wentzel-Kramers-Brillouin),E U(x),1.5 WKB method (Wentzel-Kr
13、amers-Brillouin),a1,b1 region,1.5 WKB method (Wentzel-Kramers-Brillouin),E U(x),Asymptotic solutions,1.5 WKB method (Wentzel-Kramers-Brillouin),1.5 WKB method (Wentzel-Kramers-Brillouin),1.5 WKB method (Wentzel-Kramers-Brillouin),b2,a2 region,1.5 WKB method (Wentzel-Kramers-Brillouin),This is the Bo
14、hr-Sommerfeld quantized condition,1.5 WKB method (Wentzel-Kramers-Brillouin),Example 2: Barrier penetration,1.5 WKB method (Wentzel-Kramers-Brillouin),Barrier penetration,1.5 WKB method (Wentzel-Kramers-Brillouin),Barrier penetration,1.5 WKB method (Wentzel-Kramers-Brillouin),Barrier penetration,1.5 WKB method (Wentzel-Kramers-Brillouin),Barrier penetration,1.5 WKB method (Wentzel-Kramers-Brillouin),Connection formulae (dU/dx0),1.5 WKB method (Wentzel-Kramers-Brillouin),
