Spin-orbit interaction

Could you please do the problem attached? Thank you.

Muonic hydrogen atom

Could you please do the problem attached? Thank you.

Time evolution of an electron spin in a magnetic field.

See attached file.

product of unitary operators

Show that a product of unitary operators is unitary.

vectors

Please see the attached file for the full problem statement, and please show all steps in the solution.

linear independence of vectors in the vector space of real 2 x 2 matrices

Please see the attached file for the full problem statement, and please show all steps in the solution.

vector spaces of functions

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vector space: null vector and inverse of a vector

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eigenvalues, eigenvectors, and other properties of the given matrix

Please see the attached file for full statements of the problems, and please show all steps in their solutions.

Eigenvalues and eigenvectors of the identity operator

Please see the attached file for the full problem statement, and please show all steps in your solution.