复旦量子力学讲义qmapter-PPT精品
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2020/7/30
§3.3 solutions of the free particle
2020/7/30
§3.3 solutions of the free particle
➢Discussion ➢Positive energy state (λ=+1) ➢Negative energy state (λ=-1) ➢Eigenstates of momentum p
Ep,1 c2p2m2c4 Ep,1 c2p2m2c4
2020/7/30
§3.3 solutions of the free particle
➢Orbital angular momentum is not conserved
2020/7/30
§3.1 Klein – Gordon equation
2020/7/30
§3.1 Klein – Gordon equation
2020/7/30
§3.1 Klein – Gordon equation
2020/7/30
§3.2 Dirac equation
➢How to overcome the negative probability difficulty
2020/7/30
§3.1 Klein – Gordon equation
➢With electromagnetic field
2020/7/30
§3.1 Klein – Gordon equation
2020/7/30
§3.1 Klein – Gordon equation
➢Covariant form
2020/7/30
§3.1 Klein – Gordon equation
2020/7/30
§3.1 Klein – Gordon equation
2020/7/30
§3.1 Klein – Gordon equation
➢Discussion ➢Negative energy instable
† , jkc†k
2020/7/30
§3.3 solutions of the free particle
2020/7/30
§3.3 solutions of the free particle
2020/7/30
§3.3 solutions of the free particle
2020/7/30
§3.3 solutions of the free particle
2020/7/30
§3.3 solutions of the free particle
2020/7/30
§3.3 solutions of the free particle
2020/7/30
§3.3 solutions of the free particle
2020/7/30
§3.1 Klein – Gordon equation
➢Negative probability
* 2 2 *c 1 2(* 2 t 2 2 t2*)
2020/7/30
§3.1 Klein – Gordon equation
2020/7/30
§3.1 Klein – Gordon equation
2020/7/30
§3.2 Dirac equation
➢4 anti-commute matrices α and β 4×4 matrices
2020/7/30
§3.2 Dirac equation
2020/7/30
§3.2 Dirac equation
➢Conservation law of the probability flux
Chapter 3 Relativistic Quantum Mechanics
2020/7/30
2020/7/30
Introduction
➢Non-relativistic quantum mechanics relativistic quantum mechanics
➢Schrödinger equation ➢Klein-Gordon equation S ~ integer ➢Dirac equation S ~ half integer ➢Spin is automatically contained in Dirac
2020/7/30
§3.2 Dirac equation
2020/7/30
§3.2 Dirac equation
2020/7/30
§3.2 Dirac equation
2020/7/30
§3.2 Dirac equation
➢The condition for α and β
1) They must follow the relation
➢Non-relativistic limit: K-G eq Sch eq
2020/7/30
§3.1 Klein – Gordon equation
2020/7/30
§3.1 Klein – Gordon equation
2m ic2['( t'im c2')'*( t'im c2')] '*'*
2020/7/30
§3.2 Dirac equation
i† t ici 31† k x km c2
i
wk.baidu.com†i
t
3
ci1xk
† km c2
i t† ici 31 xk†km c2
2020/7/30
§3.2 Dirac equation
i
()i
t
ci 31 xk(k)
E2c2p2m2c4
2) Operator H must be Hermitian 3) Lorentz invariance
2020/7/30
§3.2 Dirac equation
2020/7/30
§3.2 Dirac equation
2020/7/30
§3.2 Dirac equation
equation
2020/7/30
§3.1 Klein – Gordon equation
➢Lorentz transormation time, space are of the same weight
➢K – G equation
2020/7/30
§3.1 Klein – Gordon equation
§3.3 solutions of the free particle
2020/7/30
§3.3 solutions of the free particle
➢Discussion ➢Positive energy state (λ=+1) ➢Negative energy state (λ=-1) ➢Eigenstates of momentum p
Ep,1 c2p2m2c4 Ep,1 c2p2m2c4
2020/7/30
§3.3 solutions of the free particle
➢Orbital angular momentum is not conserved
2020/7/30
§3.1 Klein – Gordon equation
2020/7/30
§3.1 Klein – Gordon equation
2020/7/30
§3.1 Klein – Gordon equation
2020/7/30
§3.2 Dirac equation
➢How to overcome the negative probability difficulty
2020/7/30
§3.1 Klein – Gordon equation
➢With electromagnetic field
2020/7/30
§3.1 Klein – Gordon equation
2020/7/30
§3.1 Klein – Gordon equation
➢Covariant form
2020/7/30
§3.1 Klein – Gordon equation
2020/7/30
§3.1 Klein – Gordon equation
2020/7/30
§3.1 Klein – Gordon equation
➢Discussion ➢Negative energy instable
† , jkc†k
2020/7/30
§3.3 solutions of the free particle
2020/7/30
§3.3 solutions of the free particle
2020/7/30
§3.3 solutions of the free particle
2020/7/30
§3.3 solutions of the free particle
2020/7/30
§3.3 solutions of the free particle
2020/7/30
§3.3 solutions of the free particle
2020/7/30
§3.3 solutions of the free particle
2020/7/30
§3.1 Klein – Gordon equation
➢Negative probability
* 2 2 *c 1 2(* 2 t 2 2 t2*)
2020/7/30
§3.1 Klein – Gordon equation
2020/7/30
§3.1 Klein – Gordon equation
2020/7/30
§3.2 Dirac equation
➢4 anti-commute matrices α and β 4×4 matrices
2020/7/30
§3.2 Dirac equation
2020/7/30
§3.2 Dirac equation
➢Conservation law of the probability flux
Chapter 3 Relativistic Quantum Mechanics
2020/7/30
2020/7/30
Introduction
➢Non-relativistic quantum mechanics relativistic quantum mechanics
➢Schrödinger equation ➢Klein-Gordon equation S ~ integer ➢Dirac equation S ~ half integer ➢Spin is automatically contained in Dirac
2020/7/30
§3.2 Dirac equation
2020/7/30
§3.2 Dirac equation
2020/7/30
§3.2 Dirac equation
2020/7/30
§3.2 Dirac equation
➢The condition for α and β
1) They must follow the relation
➢Non-relativistic limit: K-G eq Sch eq
2020/7/30
§3.1 Klein – Gordon equation
2020/7/30
§3.1 Klein – Gordon equation
2m ic2['( t'im c2')'*( t'im c2')] '*'*
2020/7/30
§3.2 Dirac equation
i† t ici 31† k x km c2
i
wk.baidu.com†i
t
3
ci1xk
† km c2
i t† ici 31 xk†km c2
2020/7/30
§3.2 Dirac equation
i
()i
t
ci 31 xk(k)
E2c2p2m2c4
2) Operator H must be Hermitian 3) Lorentz invariance
2020/7/30
§3.2 Dirac equation
2020/7/30
§3.2 Dirac equation
2020/7/30
§3.2 Dirac equation
equation
2020/7/30
§3.1 Klein – Gordon equation
➢Lorentz transormation time, space are of the same weight
➢K – G equation
2020/7/30
§3.1 Klein – Gordon equation