The kinetic energy operator for an electron is p²/2m. Use eqn 1.41 to show that this can be rewritten (1.79) 2me If a magnetic field is applied one must replace p by p + eA. With the aid of eqn 1.40, show that this replacement substituted into eqn 1.79 leads to kinetic energy of the form (p + eA)? + gµBB · S (1.80) 2me where the g-factor in this case is g = 2. (Note that in this problem you have to be careful how you apply eqn 1.40 and 1.41 because p is an operator and will not commute with A.)
The kinetic energy operator for an electron is p²/2m. Use eqn 1.41 to show that this can be rewritten (1.79) 2me If a magnetic field is applied one must replace p by p + eA. With the aid of eqn 1.40, show that this replacement substituted into eqn 1.79 leads to kinetic energy of the form (p + eA)? + gµBB · S (1.80) 2me where the g-factor in this case is g = 2. (Note that in this problem you have to be careful how you apply eqn 1.40 and 1.41 because p is an operator and will not commute with A.)
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The kinetic energy operator for an electron is P2/2m. use (σ . a)2=|a|2 to show that this can be written (σ . P)2/2me if a magnetic field is applied one must replace P by P+eA. with the aid of (σ . a)(σ . b)=a . b + iσ . (a×b) , show that this replacement substituted into (σ . P)2/2me leads to kinetic energy of the form (P + eA)2/2me + gµBB.S where the g-factor, in this case, is g=2.(Note that in this problem you have to be careful how you apply (σ . a)(σ . b)=a . b + iσ . (a×b) and (σ . a)2=|a|2 because P is an operator and will not commute with A)
Transcribed Image Text:(в а) (а b) — а b +ia -(a x b)
(1.40)
(o . a)? = la|?.
(1.41)
Transcribed Image Text:The kinetic energy operator for an electron is p²/2m. Use
eqn 1.41 to show that this can be rewritten
(1.79)
2me
If a magnetic field is applied one must replace p by p+
eA. With the aid of eqn 1.40, show that this replacement
substituted into eqn 1.79 leads to kinetic energy of the
form
(p + eA)2
+ guBB. S
(1.80)
2me
where the g-factor in this case is g = 2. (Note that in this
problem you have to be careful how you apply eqn 1.40
and 1.41 because p is an operator and will not commute
with A.)
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