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PHYS_342_hmwrk4 - PHYS342 FallSemester2011...

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1 PHYS 342 Fall Semester 2011 Solutions: Homework No. 4 Due: October 14, 2011 1. In an experiment, the speed of an electron is measured to be 6.0x10 5 m/s. Since all measurements have an uncertainty associated with them, in this case say the electron speed is only measured to an accuracy of 1.0x10 4 m/s. This implies that the uncertainty in the speed of the electron is therefore 2x10 4 m/s. According to quantum mechanics, what is the size of the smallest region in space in which the electron could be found?
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2 2. Consider the wave form shown below Assume the wave can be represented by the formula By inspection, what are your best guesses for B, C, 1 and 2 ? Assume 2 > 1 . 1 2 2 2 sin sin x x A B C 3 2 1 0 1 2 3 0.00 0.01 0.02 0.03 0.04 0.05 0.06 Amplitude, A x (in m)
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3 3. a) Write down the solution to the angular Schrödinger’s Equation for the m=+1, =1 quantum state of atomic hydrogen. b) Verify that the spherical harmonic Y 11 ( ϑ , φ ) you wrote in a) satisfies the angular Schrödinger’s Equation
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