Free particle – travelling wave packet
Required math: calculus Required physics: Schrödinger equation References: Griffiths, David J. (2005), Introduction to Quantum Mechanics, 2nd Edition; Pearson Education – Problem 2.43. We’ve looked at...
View ArticleEnergy-time uncertainty principle: Gaussian free particle
Required math: calculus Required physics: Schrödinger equation References: Griffiths, David J. (2005), Introduction to Quantum Mechanics, 2nd Edition; Pearson Education – Problem 3.19. As another...
View ArticleFree particle in momentum space
Required math: calculus Required physics: Schrödinger equation References: Griffiths, David J. (2005), Introduction to Quantum Mechanics, 2nd Edition; Pearson Education – Problem 3.40. Since the...
View ArticleFree particle revisited: solution in terms of a propagator
References: Shankar, R. (1994), Principles of Quantum Mechanics, Plenum Press. Section 5.1, Exercise 5.1.1. Having reviewed the background mathematics and postulates of quantum mechanics as set out by...
View ArticleFree particle in the position basis
References: Shankar, R. (1994), Principles of Quantum Mechanics, Plenum Press. Section 5.1, Exercise 5.1.2. In quantum mechanics, the free particle has degenerate energy eigenstates for each energy...
View ArticlePropagator for a Gaussian wave packet for the free particle
References: Shankar, R. (1994), Principles of Quantum Mechanics, Plenum Press. Section 5.1, Exercise 5.1.3. The propagator for the free particle is We can find its matrix elements in position space by...
View ArticlePath integral formulation of quantum mechanics: free particle propagator
Shankar, R. (1994), Principles of Quantum Mechanics, Plenum Press. Chapter 8. Although all the non-relativistic quantum mechanics we’ve done so far has started with the Schrödinger equation, a...
View ArticleFree particle propagator from a complete path integral
Shankar, R. (1994), Principles of Quantum Mechanics, Plenum Press. Chapter 8. Section 8.4. We’ve seen that the free-particle propagator can be obtained in the path integral approach by using only the...
View ArticleFree particle in spherical coordinates – finding the solutions
Shankar, R. (1994), Principles of Quantum Mechanics, Plenum Press. Chapter 12, Exercise 12.6.6. [If some equations are too small to read easily, use your browser’s magnifying option (Ctrl + on Chrome,...
View ArticleFree particle moving in the z direction
Shankar, R. (1994), Principles of Quantum Mechanics, Plenum Press. Chapter 12, Exercise 12.6.10. [If some equations are too small to read easily, use your browser’s magnifying option (Ctrl + on Chrome,...
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