(Shankar) Expectation Value and Uncertainty of Position and Momentum for the free particle (Shankar's 5.1 free particle + Expectation Value and Uncertainty of Momentum)

This article covers Shankar's "5.1. the free particles" and includes the derivation process of each equation skipped by Shankar. Additionally, the part that calculates the expectation value and Uncertainty of Momentum is included.

In particular, most of the contents of the expectation value of momentum were referred to Golwala's Lecture note.

<Reference >

1. Shankar's Book "Principles of Quantum Mechanics"  5.1. The Free Particle

2. Sunil Golwala's Lecture note "Quantum Mechanics"

   https://www.astro.caltech.edu/~golwala/ph125ab/index.html

3. Griffiths' Book “Introduction to quantum mechanics”