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Physics 633 Exam 1 Please show all significant steps clearly in all problems.
 

Summary: Physics 633 Exam 1
Please show all significant steps clearly in all problems.
1. In class, we applied Noether's theorem to relativistic bosons and fermions. Let us now ap-
ply it to nonrelativistic spin 1/2 fermions, for which the field operator (x) is a 2-component
spinor and the Lagrangian density is
L =
(x) ih

t
- h (-x ) (x) (1)
with
h (-x ) = -
h2
2m
2
+ V (-x ) . (2)
(a) (6) By extremalizing the action S, determine the equations of motion for the quantized
fields (x) and
(x) .
(b) (6) Calculate the conjugate momentum fields and

  

Source: Allen, Roland E. - Department of Physics and Astronomy, Texas A&M University

 

Collections: Physics