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Chapter 5: Q59E (page 191)
Determine the expectation value of the position of a harmonic oscillator in its ground state.
The expectation value of harmonic oscillator in ground state is 0.
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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?
The uncertainty in a particle's momentum in an infinite well in the general case of arbitrary is given by .
The figure shows a potential energy function.
(a) How much energy could a classical particle have and still be bound?
(b) Where would an unbound particle have its maximum kinetic energy?
(c) For what range of energies might a classical particle be bound in either of two different regions?
(d) Do you think that a quantum mechanical particle with energy in the range referred to in part?
(e) Would be bound in one region or the other? Explain.
equation (5-33). The twosolutionsare added in equal amounts. Show that if we instead added a different percentage of the two solutions. It would not change the important conclusion related to the oscillation frequency of the charge density.
Quantization is an important characteristic of systems in which a particle is bound in a small region. Why "small," and why "bound"?
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