Write the eigenfunction and eigenvalue of a 2D particle-in-a-box whose dimensions are a and b, respectively. b) Assuming a=b, how many eigenfunctions have an eigenvalue of E=13h2/(8ma2)? What are the values of (nx,ny) of these eigenstates? c) Under what limit is the 3D particle in a box consistent with the 2D particle in a box? How many eigenstates of a 3D particle in a box have eigenvalue of E=38h2/(8ma2) if a=b=c? Would changing c change this number?

Write the eigenfunction and eigenvalue of a 2D particle-in-a-box whose dimensions are a and b, respectively. b) Assuming a=b, how many eigenfunctions have an eigenvalue of E=13h2/(8ma2)? What are the values of (nx,ny) of these eigenstates? c) Under what limit is the 3D particle in a box consistent with the 2D particle in a box? How many eigenstates of a 3D particle in a box have eigenvalue of E=38h2/(8ma2) if a=b=c? Would changing c change this number?