Question

8. The time independent Schrödinger equation (TISE) in one-dimension where m is the mass of the particle, E ita energy, (z) the potential (a) Consider a particle moving in a constant pote E> Vo, show that the following wave function is a solution of the TISE and determine the relationahip betwoen E an zero inside the well, ie. V(2)a 0foros L, and is infinite ou , ie, V(x)-w (4) Assuming (b) Consider an infinite square well with walls at 1-0 and z = L. The potential is tside the well, i.e. V(a)oo for < 0 and z L. What are he boundary conditions which must be satisfied by physical wave-functions of a particlke in this well? for s (c) By considering boundary conditions determine the allowed values of B and r. (d) Hence show that the allowed energies for a particle in the well are physical wave-functions for a particle in the well. 15) 8mL2 where integer n > 0. Why is the n- 0 case not an allowed energy? a width of 1 Angstrom, what is the difference in energy between the lowest and second lowest energy states of the electron? What wavelength of light would be transmitted or absorbed in a transition between these states? (e) If an electron is in an infinite square well as described in part (b) and the well has 4 CONTINUED PHAS1202/2013

Answer 1

2 m 0 b2 dm2 Barda ad.tous up:o.at aco t ゲ 2 .-68 -3x6625メlo 8x9.20 09.88 A