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Statistical mechanics in quantum theory: counting boson states
References: Griffiths, David J. (2005), Introduction to Quantum Mechanics, 2nd Edition; Pearson Education – Problem 5.25. When working out the number of possible configurations in which identical...
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Statistical mechanics in quantum theory: Bose condensation
References: Griffiths, David J. (2005), Introduction to Quantum Mechanics, 2nd Edition; Pearson Education – Problem 5.29. We’ve seen the distribution of particles for the most probable state in the...
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Fermions and bosons: counting states
References: Griffiths, David J. (2005), Introduction to Quantum Mechanics, 2nd Edition; Pearson Education – Problem 5.33. A simple example of counting available states. We have three available...
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Bosons in the infinite square well
References: Griffiths, David J. (2005), Introduction to Quantum Mechanics, 2nd Edition; Pearson Education – Problem 6.3. An example of perturbation theory applied to the interaction between two...
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Occupation number representation; delta function as a series
References: Tom Lancaster and Stephen J. Blundell, Quantum Field Theory for the Gifted Amateur, (Oxford University Press, 2014) – Problem 3.1. We can write the hamiltonian for the harmonic oscillator...
View ArticleCreation and annihilation operators: commutators and anticommutators
References: Amitabha Lahiri & P. B. Pal, A First Book of Quantum Field Theory, Second Edition (Alpha Science International, 2004) – Chapter 1, Problems 1.1 – 1.2. As a bit of background to the...
View ArticleIdentical particles – bosons and fermions revisited
Shankar, R. (1994), Principles of Quantum Mechanics, Plenum Press. Chapter 10, Exercises 10.3.1 – 10.3.3. Although we’ve looked at the quantum treatment of identical particles as done by Griffiths,...
View ArticleCompound systems of fermions and bosons
Shankar, R. (1994), Principles of Quantum Mechanics, Plenum Press. Chapter 10, Exercise 10.3.6. In a system of identical particles, we’ve seen that if the particles are bosons, the state vector is...
View ArticleInvariance of symmetric and antisymmetric states; exchange operators
Shankar, R. (1994), Principles of Quantum Mechanics, Plenum Press. Chapter 10, Exercise 10.3.5. In a system with two particles, the state in the basis is given by where is the position of particle . We...
View ArticleFermions and bosons in the infinite square well
Shankar, R. (1994), Principles of Quantum Mechanics, Plenum Press. Chapter 10, Exercise 10.3.4. Suppose we have two identical particles in an infinite square well. The energy levels in a well of width...
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