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Chapter 5: 6CQ (page 186)

When is the temporal part of the wave function 0 ? Why is this important?

Short Answer

Expert verified

Answer:

The likelihood of discovering the probability would be 0 if the temporal part of a wave function was zero, implying that the particle would have vanished.

Step by step solution

01

Theory of wave function

The wave function ψitself has no physical significance. However, the amplitude of wave function corresponds ψto and the square of the wave functionψ relates to the photon density, the number of photons present in a region, it relates to electron density in a certain region.

02

Conclusion

Therefore, using the square of wave function, we can measure of the probability that the electron can be found within a particular tiny volume of the atom.

Hence, The likelihood of discovering the probability would be 0 if the temporal part of a wave function was zero, implying that the particle would have vanished.

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Most popular questions from this chapter

There are mathematical solutions to the Schrödinger equation for the finite well for any energy, and in fact. They can be made smooth everywhere. Guided by A Closer Look: Solving the Finite Well. Show this as follows:

(a) Don't throw out any mathematical solutions. That is in region Il (x<0), assume that (Ce+ax+De-ax), and in region III (x>L), assume thatψ(x)=Fe+ax+Ge-ax. Write the smoothness conditions.

(b) In Section 5.6. the smoothness conditions were combined to eliminate A,Band Gin favor of C. In the remaining equation. Ccanceled. leaving an equation involving only kand α, solvable for only certain values of E. Why can't this be done here?

(c) Our solution is smooth. What is still wrong with it physically?

(d) Show that

localid="1660137122940" D=12(B-kαA)andF=12e-αL[(A-Bkα)sin(kL)+(Akα+B)cos(kL)]

and that setting these offending coefficients to 0 reproduces quantization condition (5-22).

What is the probability that the particle would be found between x = 0and x = 1/a?

a) Taking the particle’s total energy to be 0, find the potential energy.

(b) On the same axes, sketch the wave function and the potential energy.

(c) To what region would the particle be restricted classically?

Where would a particle in the first excited state (first above ground) of an infinite well most likely be found?

In several bound systems, the quantum-mechanically allowed energies depend on a single quantum number we found in section 5.5 that the energy levels in an infinite well are given by, En=a1n2wheren=1,2,3.....andis a constant. (Actually, we known whata1is but it would only distract us here.) section 5.7 showed that for a harmonic oscillator, they areEn=a2(n−12), wheren=1,2,3.....(using ann−12with n strictly positive is equivalent towith n non negative.) finally, for a hydrogen atom, a bound system that we study in chapter 7,En=−a3n2, wheren=1,2,3.....consider particles making downwards transition between the quantized energy levels, each transition producing a photon, for each of these three systems, is there a minimum photon wavelength? A maximum ? it might be helpful to make sketches of the relative heights of the energy levels in each case.
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