3 Quantum Harmonic Oscillator Another form of a potential energy function that can be used to describe a molecular bond is: V(y) = where and are constants. (A) Using a Taylor Series expansion, derive an effective harmonic force constant that could be used for a harmonic oscillator approximation to the potential V(y) around the point y=0. (B) What are the eigenvalues of the QHO Hamiltonian utilizing the harmonic force constant you derived in (A)? (C) Calculate for the n-3 QHO wavefunction. You must work through the math to show your solution (either Mathematica or even/odd function relationships are suitable means of evaluating integrals). (D) Calculate for the n=3 QHO wavefunction. You must work through the math to show your solution (either Mathematica or even/odd function relationships are suitable means of evaluating integrals). (E) Calculate the commutator of [H,py] (be sure you include all terms in the QHO Hamiltonian). What does your result mean about the ability to measure H and Py simultaneously? Evaluate the following expressions numerically: <1|PrV3 >, < 2P1516 >, (F) <448|23|452>

PLEASE SOLVE WITH MATLAB. WILL GIVE LIKE!!!

Using partial derivatives, calculate the propagated uncertainty in the mass in the following case: given the centripetal force Fc = (20.0 ± 0.5) N, the angular velocity w = (29.2 ± 0.3) rad/s, and the radius R = (0.12 ± 0.01) m get the mass value,m = Fc / (w2R). Express the result in the form m = m + Δm ----------------------------------- THAT'S THE QUESTION ASKED, see the image for the answer. Also have a look at the second image, the blue one. --------------------------------------------------------------- Explain what is the 1/m just after the equals sign at the second line of the answer. Also, explain why the answer does not use the square root just like the blue image, of if it is using it. Then, say in which case should I use the partial derivate to calculate the uncertainty.

3. The classical partition function of a gas of noninteracting indistinguishable particles is written as exp{- N! 2m Z= where N is the number of particles of mass m, r, and p, are the position and the momentum of the ith particle, B = 1/(kpT), and Tis the temperature of the gas. The volume of the gas is V. (a) Find the analytic expression of the partition function of the gas. (b) Obtain the total mean energy E of the gas from the partition function. (c) Obtain the entropy S of the gas from the partition function and the total mean energy. Lexp(-x³xdx = Va Hint: