Quantum mechanics: Identical Particle

A quantum system is formed by A identical particles, each of which is ruled by the time-independent Schrodinger equation hiv = c,,, where he is a spin-independent single-particle Hamiltonian. a) Assuming that the particles are non-interacting, write the total Hamiltonian of the N-particle system. [1 point] b) What is the ground-state energy of the N-particle system if the particles have spin 0? [1 point] c) What is the total wave-function of a system formed by 3 particles with spin 0? [1 point] d) Which type of particles are they if they have spin 0? [1 point] e) What is the ground-state energy of the N-particle system if these particles have spin 1/2? Consider both cases in which N is an even (N = 2M) and an odd number (N = 2M + 1). [2 points] What is the total wave-function of a system formed by 3 particles with spin 1/2? [1 point] g) Which type of particles are they if they have spin 1/2? [1 point]