(d) The spin of particle can be observed by using external magnetic filed B = B, i +B, j + B, k. The interaction energy between the particle and magnetic field is described by the following Hamiltonian: Ĥ = -yB · § = -^(B,§, + B,„§, + B,§.) (1) where y is a positive constant called gyromagnetic ratio. Show that the matrix repre- sentation of the Hamiltonian (by |+) and |–}) is [(+|Ĥ|+) (+\Ĥ|-)] [(-||+) {-|Ħ|-)J B. 2 B+iBy B, – iB,] -B, (2) Is this operator Hermitian?
(d) The spin of particle can be observed by using external magnetic filed B = B, i +B, j + B, k. The interaction energy between the particle and magnetic field is described by the following Hamiltonian: Ĥ = -yB · § = -^(B,§, + B,„§, + B,§.) (1) where y is a positive constant called gyromagnetic ratio. Show that the matrix repre- sentation of the Hamiltonian (by |+) and |–}) is [(+|Ĥ|+) (+\Ĥ|-)] [(-||+) {-|Ħ|-)J B. 2 B+iBy B, – iB,] -B, (2) Is this operator Hermitian?
Related questions
Question
Please do D, E, and F
![(d) The spin of particle can be observed by using external magnetic filed B = B, i +B, j +
B, k. The interaction energy between the particle and magnetic field is described by the
following Hamiltonian:
Ĥ = -yB · § = -^(B,§, + B,„§, + B,§.)
(1)
where y is a positive constant called gyromagnetic ratio. Show that the matrix repre-
sentation of the Hamiltonian (by |+) and |–}) is
[(+|Ĥ|+) (+\Ĥ|-)]
[(-||+) {-|Ħ|-)J
B.
2 B+iBy
B, – iB,]
-B,
(2)
Is this operator Hermitian?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa4426dc-92c3-4ac7-bd5a-9ba1dd10b9af%2Fe3242dd5-0d43-4b29-b087-6fe7f0cee5e6%2F8t09jgl.png&w=3840&q=75)
Transcribed Image Text:(d) The spin of particle can be observed by using external magnetic filed B = B, i +B, j +
B, k. The interaction energy between the particle and magnetic field is described by the
following Hamiltonian:
Ĥ = -yB · § = -^(B,§, + B,„§, + B,§.)
(1)
where y is a positive constant called gyromagnetic ratio. Show that the matrix repre-
sentation of the Hamiltonian (by |+) and |–}) is
[(+|Ĥ|+) (+\Ĥ|-)]
[(-||+) {-|Ħ|-)J
B.
2 B+iBy
B, – iB,]
-B,
(2)
Is this operator Hermitian?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 4 images
