A. Imagine a particle free to move in the x direction. Which of the following wavefunctions would be acceptable for such a particle? In each case, give your reasons for accepting or rejecting each function. 1. ψ(x)=x2 
2. ψ(x)=1/x 
3. ψ(x)=e^−x2.

b. Imagine a particle confined to move on the circumference of a circle ('a particle on a ring'), such that its position can be described by an angle ϕ in the range 0−2π.. Which of the following wavefunctions would be acceptable for such a particle? In each case, give your reasons for accepting or rejecting each function.

1. cosϕ
2. sinϕ
3. cos(0.9ϕ).