Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
1.2 Prove the following: (i) (ii) The scalar product is invariant under unitary transformation. The trace of a matrix in invariant under unitary transformation.

1.2 Prove the following: (i) (ii) The scalar product is invariant under unitary transformation. The trace of a matrix in invariant under unitary transformation.

icon
Related questions
Question
Ass Q1: Quantum Mechanics Question 1.2 please
Question 1 1.1 Evaluate the following: (i) SxSy + SySx (ii) S²S,³S² (iii) Use the concept of parity to show whether < 3p|xsinx|2s> is zero or not 1.2 Prove the following: The scalar product is invariant under unitary transformation. (ii) The trace of a matrix in invariant under unitary transformation. 1.3 The raising (at) and lowering (a) operators of a harmonic oscillator satisfy the relations a|n >= √nn - 1 > and a+|n > = √n + 1\n + 1 >, n = 1, 2, 3, ... Obtain the matrix for at.
Transcribed Image Text:Question 1 1.1 Evaluate the following: (i) SxSy + SySx (ii) S²S,³S² (iii) Use the concept of parity to show whether < 3p|xsinx|2s> is zero or not 1.2 Prove the following: The scalar product is invariant under unitary transformation. (ii) The trace of a matrix in invariant under unitary transformation. 1.3 The raising (at) and lowering (a) operators of a harmonic oscillator satisfy the relations a|n >= √nn - 1 > and a+|n > = √n + 1\n + 1 >, n = 1, 2, 3, ... Obtain the matrix for at.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer