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# Ch2 - 2.6 Calculate the de Broglie wavelength =h/p for(a An...

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2.6 Calculate the de Broglie wavelength, λ =h/p, for: (a) An electron with kinetic energy of (i) 1.0 eV, and (ii) 100 eV. (b) A proton with kinetic energy of 1.0 eV. (c) A singly ionized tungsten atom with kinetic energy of 1.0 eV. (d) A 2000-kg truck traveling at 20 m/s. 2.17 Consider the wave function ψ (x,t) = A(sin n π x)e -j ω t for – 1 x +1. Determine A so that . 1 1 1 2 ) , ( = Ψ dx t x 2.26 Consider the particle in the infinite potential well as shown in Figure 2.11. Derive and sketch the wave functions corresponding to the four lowest energy levels. (Do not normalize the wave functions.) 2.27 Consider a three-dimensional infinite potential well. The potential function is given by V(x) = 0 for 0 < x < a, 0 < y < a, 0 < z < a, and V(x) = elsewhere. Start with Schrodinger’s wave equation, use the separation of variables technique, and show that the energy is quantized and is given by ( ) 2 2 2 2 2 2 2 z y x n n n n n n ma E z y x + + = π h , where n x = 1, 2, 3, …., n y = 1, 2, 3, …., n z = 1, 2, 3, …. 2.30 For the step potential function shown in Figure 2.12, assume that E > V 0 and that particles are incident from the

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