Question

6. For a particle in a one-dimensional box, the ground state wave function is sin What is the probability that the particle is in the right-hand half of the box? Ans: V/, or 50% а. b What is the probability that the partic le is in the middle third of the box? Ans: 0.609 or 60.9%

Answer 1

(6) Given, wave function associated with a particle in a one-timensional box, J른 편 a) By Born Interpretation, Probability is given by, P = 1 4 4*, dk V L2 here, for right hand half of the box, limit is 2 so L 12 sinta 2 J va Iva sinta JR VI P r sin2ta da C1-cos29X LI P = da - Cosant te I I L-L... L II 2 27L I L - L L2 27 2T E sin zin . LJ 4. sin 27 - sint] [ since sin h = pe 50%

If the particle Soi ronge is ! in in the midtle thind of box. to L. O So, P= I asinan . 2 cinity to VB 2 sin Ty dx - P = - cos 24. tu 43 PES I cos 2ta 13 sin 277 P = txt = 1 L 2 Isinama 37 [ sin 21 ] मा L .LT 2T = II 0.33L - 0.0058L] LL 0.324