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- Under what conditions would the operator described as multiplication by i the square root of 1 be considered a Hermitian operator?Explain why n=0 is not allowed for a particle-in-a-box.Is the uncertainty principle consistent with our description of the wavefunctions of the 1D particle-in-a-box? Hint: Remember that position is not an eigenvalue operator for the particle-in-a-box wavefunctions.
- In a plot of ||2, the maximum maxima in the plot is/are called the most probable positions. What is/are the most probable positions for a particle-in-a-box when: a n=1 b n=2 c n=3 d Do you see a trend?What is the degeneracy of an h subshell? An n subshell?A particle on a ring has a wavefunction =12eim where equals 0 to 2 and m is a constant. Evaluate the angular momentum p of the particle if p=i How does the angular momentum depend on the constant m?
- State whether the following functions are acceptable wavefunctions over the range given. If they are not, explain why not. aF(x)=x2+1,0x10 bF(x)=x+1,x+ cf(x)=tan(x),x d=ex2,x+The following operators and functions are defined: A=x()B=sin()C=1()D=10()p=4x32x2q=0.5r=45xy2s=2x3 Evaluate: a Ap b Cq c Bs d Dq e A(Cr) f A(Dq)