- 3 A Write Down The Normalized Eigen Functions For The Ground State And The First Excited States 4 X And 41 X For 1 (56.62 KiB) Viewed 22 times
3. (a) Write down the normalized eigen functions for the ground state, and the first excited states 4.(x) and 41(x) for
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3. (a) Write down the normalized eigen functions for the ground state, and the first excited states 4.(x) and 41(x) for
3. (a) Write down the normalized eigen functions for the ground state, and the first excited states 4.(x) and 41(x) for a particle of mass m in a linear harmonic oscillator potential. (b)Perform the necessary integrations to verify that wo(x) and 1(x) are normalized. (c) Show that yo(x) and 41(x) are orthogonal. (d) Show that Tvi(y) yy.(y)dy = ta where y=Vax= mo X ti 4. (a) Carry out the necessary integrations to find the following expectation values for the ground state of a particle of mass m in the harmonic oscillator potential of frequency o: (x), (x2), (p) and (p2) (b) Using the results of (a), obtain the expectation values (K) and (V) of the kinetic and potential energy, respectively. (c) Calculate the uncertainty product Ar.Ap for this state. What do you conclude from the value of the uncertainty product?
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