6. An electron in hydrogen atom is in initial statep(r, 0) = A(2µ100 + ¡Þ210 + 4Þ21–1 – 2i4211)where ynim are the eigenfunctions of the hydrogen atoma. Determine the constant Ab. What is the probability of finding the electron in the first excited state?c. Write the state p(r, t) at time t, using energy eigenvalues as En =d. Find the expectation value of L in the state (r,te. Find the expectation values of Lx and Ly in the state (r, tf. If measurement of L, led to the value -ħ what will be results of measurement ofenergy and the square of total orbital momentum immediately afterwards andwhat are their probabilities?hwn2

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6. An electron in hydrogen atom is in initial state p(r, 0) = A(24100 + iP210 + 4421-1 - 2ip211) where ntm are the eigenfunctions of the hydrogen atom a. Determine the constant A b. What is the probability of finding the electron in the first excited state? c. Write the state p(r, t) at time t, using energy eigenvalues as E hw n2

6. An electron in hydrogen atom is in initial state p(r, 0) = A(24100 + iP210 + 4421-1 - 2ip211) where ntm are the eigenfunctions of the hydrogen atom a. Determine the constant A b. What is the probability of finding the electron in the first excited state? c. Write the state p(r, t) at time t, using energy eigenvalues as E hw n2

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter28: Quantum Physics

Section: Chapter Questions

Problem 13P

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6. An electron in hydrogen atom is in initial state Þ(r, 0) = A(2410o + iÞ210 + 421–1 – 2ib211) where wnim are the eigenfunctions of the hydrogen atom a. Determine the constant A b. What is the probability of finding the electron in the first excited state? hw = - n2 c. Write the state Þ(r, t) at time t, using energy eigenvalues as En d. Find the expectation value of L in the state Þ(r,t e. Find the expectation values of Lx and Ly in the state (r, t f. If measurement of Lz led to the value –ħ what will be results of measurement of energy and the square of total orbital momentum immediately afterwards and what are their probabilities?
The chemical potential of an ideal gas Use as ƏN E,V V S(E,V, N) = Nk| ln N 3 In 2 3Νπh? a. Derive the dependence of the chemical potential u on E, V, and N for an ideal classical gas. b. Use 3 E = -NkT. to determine µ(T, V, N)
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