Physics 550 Problem Set ff2 Due Mon. Sept. 23’h Note: o Do not write up a solution that is essentially no more than a string of equations. Use language to show that you know what the meaning of your solution ii. When grading I am looking for understanding and will not consider strings of equations as indicating understanding. o Avoid the temptation of trying to do the entire assignment the night before it is due. This one is impossible to do that way. -You learn much less that way and it is rarely helpful for you. 1. Find the order of the group of transformations that leaves an equilateral triangle invariant. Identify the complete set of group elements, find a matrix representation, and then construct the multiplication table.’ What is the common name of this group? 2. Show that the two expressions below are equivalent.JrV where (1) (2) (3) (p,) : I* Oo.-e.(p,)p*e(p,) (p,) : l* o* v.@1Pv@) o(r,l : hf o* “i*o(a) *r,l What conditions are necessary for this equivalence?. -;t5s”)’# ,1 “-*tr3) perive the position-momentum Heisenberg Uncertainty Principle. What is the value rf i’ of L,rA,p* for the Gaussian wave packet ,t @):@fur””el-@#A+f,no@-,,)] e) Suppose the variance, 02 is the complex number o2o + lol, then what is the value of A,rLp* (be careful about normalization)? What is thL soluiion to the Schrodinger equation of a free particle it tlt(r) is taken as the initial condition ,b(*,t:0)? 4. For the wave function, ,h@) : csexp(i,psrlfr)lr/AT$, find the normalization con_ stant c6 and the probability of finding the particle in the interval +”ltfg. what is the mean momentum?