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Answer all sections
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Answer all sections
Answer all sections
(a) State four rules that wavefunctions must satisfy in order to be valid, illustrating each rule with a sketched diagram. (a marks) ( (b) A particle moving in a potential well, V = kr?, can be described using the wavefunction will. Equation Q2.a. well = N, Xeux Equation 22.a 0 Sketch (1 mark) 6) What is the significance of the quantity "Y? (2 marks) (II) Sketch V Y for (2 marks) (W) Indicate on your sketch the distance from equilibrium where the particle is most likely to be found. (1 mark) W What is the significance of the quantity N, ? (2 marks) (c) In order to model the behaviour of a particle, a trial wavefunction et Equation Q2.b, comprised of the sum of three functions was proposed. hest = N. (62" - 3e-3x - 25.) Equation Q2.b 0 Show that the functions of the form, els are eigenfunctions of the momentum operator, p =-th(d/dr). (3 marks) ) What is the probability that one measurement of the particle's momentum gives a result of -3? (3 marks) (II) What is the expectation value for momentum for this system? (3 marks) (
(a) State four rules that wavefunctions must satisfy in order to be valid, illustrating each rule with a sketched diagram. (a marks) ( (b) A particle moving in a potential well, V = kr?, can be described using the wavefunction will. Equation Q2.a. well = N, Xeux Equation 22.a 0 Sketch (1 mark) 6) What is the significance of the quantity "Y? (2 marks) (II) Sketch V Y for (2 marks) (W) Indicate on your sketch the distance from equilibrium where the particle is most likely to be found. (1 mark) W What is the significance of the quantity N, ? (2 marks) (c) In order to model the behaviour of a particle, a trial wavefunction et Equation Q2.b, comprised of the sum of three functions was proposed. hest = N. (62" - 3e-3x - 25.) Equation Q2.b 0 Show that the functions of the form, els are eigenfunctions of the momentum operator, p =-th(d/dr). (3 marks) ) What is the probability that one measurement of the particle's momentum gives a result of -3? (3 marks) (II) What is the expectation value for momentum for this system? (3 marks) (