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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...

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Energy-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...

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Free 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...

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Free 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...

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Free 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...

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Propagator 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...

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Path 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...

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Free 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...

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Free 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,...

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Free 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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