Demonstrate the separation of variables technique applied to equation (1) in order to separate the wave equation into two ordinary differential equations (ODEs).
Question 2 [15 marks]
Write the possible solutions to the time-dependent ODE for ψ(t) for
• positive,
• zero,
• negative
values of the constant, c = c2. Discuss why only the negative values of the constant can produce physically viable solutions.
Find the general solution for ψ(t), if it is known there are infinitely many c values that satisfy the solution.
Question 3 [10