2. In class we solved the harmenic oncillatsr pretlem. The wavefinctiars are where y=0,1,2, Hernite polynomials Hr(y) lave the following recuetion selationshipt. Hv+1(y)=2yHv(y)2vHe1(y) GivenNv=(a1/22e+1)74 1. Whe this information io dtain 2(y) and 3(y). b. Determine the sodes in these wavefunctivat $2(y) nades: 3(y) nodes: c. Detcrmine the points of masimum prohubilitiss for 2(y). ledieate ahat happens as v increases and w try. c. Met 2(y) and f(y) ento scparane potential eharily diagrams as dhren belles, On the ploe of $2(y) indicale where the modes ade and citcke the clasaical turning peints. Try to he accurate in your plot along the y.ums asing the data ebtained in b. c. and abeve. For the 12(y) plot indicate the maxima, apain trying no he aceurde selative ao the y-axis. f. Since the wavefunctioes ef the hannonic escillator are hocth entheginul and nemalined v(y)y(y)dy=rr=0v=wSp=1w=v Theve facts can be roulity chockod. i) If v= even and v= odd then clearly v(y)v(y)dy=0 However if both are even or odd the integral must be done. Show by explicit integration that 0(y)2(y)dy=0 ii) Similarly show 0(y)0(y)dy=2(y)2(y)dy=1 by explicit integration. 2. In class we solved the harmenic oncillatsr pretlem. The wavefinctiars are where y=0,1,2, Hernite polynomials Hr(y) lave the following recuetion selationshipt. Hv+1(y)=2yHv(y)2vHe1(y) GivenNv=(a1/22e+1)74 1. Whe this information io dtain 2(y) and 3(y). b. Determine the sodes in these wavefunctivat $2(y) nades: 3(y) nodes: c. Detcrmine the points of masimum prohubilitiss for 2(y). ledieate ahat happens as v increases and w try. c. Met 2(y) and f(y) ento scparane potential eharily diagrams as dhren belles, On the ploe of $2(y) indicale where the modes ade and citcke the clasaical turning peints. Try to he accurate in your plot along the y.ums asing the data ebtained in b. c. and abeve. For the 12(y) plot indicate the maxima, apain trying no he aceurde selative ao the y-axis. f. Since the wavefunctioes ef the hannonic escillator are hocth entheginul and nemalined v(y)y(y)dy=rr=0v=wSp=1w=v Theve facts can be roulity chockod. i) If v= even and v= odd then clearly v(y)v(y)dy=0 However if both are even or odd the integral must be done. Show by explicit integration that 0(y)2(y)dy=0 ii) Similarly show 0(y)0(y)dy=2(y)2(y)dy=1 by explicit integration