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Chapter 5: Q24E (page 187)
An electron in the n=4 state of a 5 nm wide infinite well makes a transition to the ground state, giving off energy in the form of photon. What is the photon鈥檚 wavelength?
The wavelength of the photon is .
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Calculate the uncertainty in the particle鈥檚 momentum.
A study of classical waves tells us that a standing wave can be expressed as a sum of two travelling waves. Quantum-Mechanical travelling waves, discussed in Chapter 4, is of the form . Show that the infinite well鈥檚 standing wave function can be expressed as a sum of two traveling waves.
Consider the delta well potential energy:
Although not completely realistic, this potential energy is often a convenient approximation to a verystrong, verynarrow attractive potential energy well. It has only one allowed bound-state wave function, and because the top of the well is defined as U = 0, the corresponding bound-state energy is negative. Call its value -E0.
(a) Applying the usual arguments and required continuity conditions (need it be smooth?), show that the wave function is given by
(b) Sketch and U(x) on the same diagram. Does this wave function exhibit the expected behavior in the classically forbidden region?
Write out the total wave function.For an electron in the n=3 state of a 10nm wide infinite well. Other than the symbols a and t, the function should include only numerical values?
Question: the operator for angular momentum about the z-axis in spherical polar coordinate is .find the function that would have a well-defined z-component of angular momentum.
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