a) Provide a physical explanation for the shape of the wavefunction for a particle in box with changes inparticle mass and box width. b) Explain for the energy of the particle in box with changes in particle mass and box width. c) What causes the particle to have discrete (quantized energies)? Hint: The free particle Schrodinger equation is the same as the particle in a box wavefunction, but its energies are not quantized. d) You have non-interacting (ideal gas) molecules of mass m in a vessel of width L. You compress the vessel adiabatically (in QM, this means, you compress slowly so that the particles stay in their same quantum states as you compress). Explain how much work was done to compress the gas. Did the temperature change?

Fig: 1

Fig: 2

Fig: 3

Fig: 4