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- For a particle in a state having the wavefunction =2asinxa in the range x=0toa, what is the probability that the particle exists in the following intervals? a x=0to0.02ab x=0.24ato0.26a c x=0.49ato0.51ad x=0.74ato0.76a e x=0.98ato1.00a Plot the probabilities versus x. What does your plot illustrate about the probability?What is the degeneracy of an h subshell? An n subshell?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.
- Show that the normalization constants for the general form of the wavefunction =sin(nx/a) are the same and do not depend on the quantum number n.Under what conditions would the operator described as multiplication by i the square root of 1 be considered a Hermitian operator?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?
- 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?In exercise 10.41a, the wavefunction is not normalized. Normalize the wavefunction and verify that it still satisfies the Schrdinger equation. The limits on x are 0 and 2. How does the expression for the energy eigenvalue differ?A particle on a ring has a wavefunction =eim, where =0to2 and m is a constant. a Normalize the wavefunction, where d is d. How does the normalization constant depend on the constant m? b What is the probability that the particle is in the ring indicated by the angular range =0to2/3? Does this answer make sense? How does the probability depend on constant m?
- For a system consisting of three particles in 3D, on what variables does the time-independent wave function c depend?Write a 1-Dim Schrodinger Equation that includes the total energy Hamiltonian operator and the electronic energy expression.For a particle in a one-dimensional box, show that the wavefunctions ψ1 and ψ3 are orthogonal.