20082ee2_1_homework%208_08

20082ee2_1_homework%208_08 - . . . . . . . . . . . . . . ....

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Unformatted text preview: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EE2 Physics for Electrical Engineers Homework #8 I. What is a wave function of the electron in quantum mechanics? How is a so called electron cloud related to the wave function? II. Write the time dependent Schrdinger equation for a free electron moving in the x direction. Write a solution of the equation for an electron of wavelength . III. Write the time dependent Schrdinger equation for the electron of a hydrogen atom. Write the corresponding time independent Schrdinger equation. Finally write the general form of the wave functions for the orbital in hydrogen atom. IV. The normalized wave function of the 1s orbital in hydrogen atom can be written as a r e a / 2 / 3 100 1 1 = , where a is the Bohr radius. Plot the wave function along the radial direction and then plot the probability density of finding the electron at radial distance r along the radial direction. electron at radial distance r along the radial direction....
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