Question

6. (Extra Credit: 6 Points) Consider two noninteracting particles of mass m in an infinite square well of width L. For the case with one particle in the single-particle state In) and the other in the state k) (nメk), calculate the expectation value of the squared inter-particle spacing (71-72) , assuming (a) the particles are distinguishable, (b) the particles are identical in a symmetrical spatial state, and (c) the particles are identical in an anti-symmetric spatial state. Use Dirac notation as far as you can, but you will have to some integrals (feel free to do the integrals numerically or use integration tables). Evaluate these expressions for the case where n 1 and k 2 (the first excited state).

Answer 1

Suppose we have two non-interactih? ma ha in-finie pae h 1 and k-2. Similarly, c z Cs Scanned with CamScanner

a C 3 2 Case b_ idantical botens aure 2 a. 2 Scanned with CamScanner

Case 3 ideical fes mions Only d fference for si2n of Jast /m here n 3 we get same expr eMion cu fordistinguisha㎘eputa Cs Scanned with CamScanner