Hermite Polynomials ( y ? ? )

1

• Hermite Polynomials ( y ? ? )
• Powers of y alternate even odd
• Successive terms alternate sign ? oscillatory
• vth order v zeros v nodes

Complete wave functions include gaussian
factor ? (k µ)½/? ß

• Similar to P in a B
• Symmetric or anti-symmetric about minimum
• Probability gt 0 in classically forbidden
• ?o ?o max at center!!!???
• Classically what do we expect?
• 5) Consider very large v probability higher at
• classical turning points agrees with
  classical
• 6) ? are orthogonal