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Indicate which of these expressions yield eigenvalue equations, and if so indicate the eigenvalue.
(a)
(c)
(e)
(g)
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Chapter 10 Solutions
Physical Chemistry
- Indicate which of these expressions yield an eigenvalue equation, and if so indicate the eigenvalue. a ddxcos4xb d2dx2cos4x c px(sin2x3)d x(2asin2xa) e 3(4lnx2), where 3=3f ddsincos g d2d2sincosh ddtanarrow_forward5. Consider a particle constrained to move in one dimension described by the wavefunction v (x) = Ne2** (a) Determine the normalization constant (b) Is the wavefunction an eigenfunction of d? +16x? dx? (c) Calculate the probability of finding the particle anywhere along the negative x-axisarrow_forward(a) For a particle in the stationary state n of a one dimensional box of length a, find the probability that the particle is in the region 0xa/4.(b) Calculate this probability for n=1,2, and 3.arrow_forward
- 2.) The function, f(x) = 3X² - 1, is an eigenfunction of the operator, A = - (1- x)(d²/ dx²) + 2x(d /dx). Find the eigenvalue corresponding to this eigenfunction.arrow_forwardThe given wave function for the hydrogen atom is y =w,00 +210 + 3y2 · Here, ypim has n, 1, and m as principal, orbital, and magnetic quantum numbers respectively. Also, yim an eigen function which is normalized. The expectation value of L in the state wis, is 9h? (a) 11 (b) 11h? 20 (c) 11 (d) 21ħ?arrow_forwardThe largest known element, francium, has an atomic diameter of 540 pm. What is the minimum uncertainty in the momentum of a a francium electron if the uncertainty in its position is taken to be the diamter of the atom? (pico = 10-12)arrow_forward
- If we measure L₂ of a particle whose state function is an eigenfunction of L² with eigenvalue 6ħ², which is not a possible outcome of the measurement? ○ 3ħ 2ħ 0 O ħ -ħarrow_forwardparticle is confined to a one-dimensional box of length L. Deduce the location of the posit ions with in the box at which the particle is most likely to be found when the quantum number of the particle is (a) n = 1. (b) n = 2. and(c) n = 3.arrow_forwardHow many eigenstates of a 3D particle in a box have eigenvalue of E=38h2/(8ma2) if a=b=c? Would changing c change this number?arrow_forward
- Imagine a particle free to move in the x direction. Which of the following wavefunctions would be acceptable for such a particle? In each case, give your reasons for accepting or rejecting each function. (1) Þ(x) = x²; (iv) y(x) = x 5. (ii) ¥(x) = ; (v) (x) = e-* ; (iii) µ(x) = e-x²; (vi) p(x) = sinxarrow_forwardFind the eigenvalue of operating on the function f(x) = Asin(nx) + Bcos(mx) with the following operator: P = d²/dx2 What must be the value of the constants A, B, m and n be to make the function an eigenfunction of this operator? 1.arrow_forwardYou are given a free particle (no potential) Hamiltonian ÎI - dependent wave-functions = ₁(x, t) V₂(x, t) = -it 2h² m = ħ² d² 2m dx2 sin(27x)e-it 2 sin(x)eit + sin(2x)e¯ hn 2 • Are V₂(x, 0) eigenfunctions of Ĥ ? (give explanation for each case) and two time- -it 2hr 2 m (1) (2)arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,Introductory Chemistry: A FoundationChemistryISBN:9781337399425Author:Steven S. Zumdahl, Donald J. DeCostePublisher:Cengage Learning
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