Chapter 38: Q86P (page 1185)

Show that ${| ψ |}^{2} = {| ψ |}^{2}$ , with related as in Eq. 38-14. That is, show that the probability density does not depend on the time variable.

Short Answer

Expert verified

The value 1 is does not depend on the time variable that shows that the probability density does not depend on the time variable.

Step by step solution

Determine the concept and the formula

In the year 1900, derived a formula that shows the relationship between all the wavelength and all the temperatures and that is given as Equation 38-14 in book and also known as the Planck’s radiation law

$S (λ) = \frac{2 π c^{2} h}{λ^{5}} \frac{1}{e^{\frac{h c}{λ K t}} - 1}$

Here, h is the Planck constant, k is the Boltzmann constant, and T is the temperature of the radiating surface (in kelvins), $λ$ is wavelength S is thermal radiation.

Determine the derivation as:

By referring the equation number 38-14 solve for the derivation as:

$\begin{array}{rcl} {|ψ|}^{2} & = & {|e^{i k x}|}^{2} \\ {|ψ|}^{2} & = & (e^{i k x}) * (e^{i k x}) = e^{- i k x} e^{i k x} \\ {|ψ|}^{2} & = & e^{0} = 1 \\ {|ψ|}^{2} & = & {|ψ|}^{2} \end{array}$

The value 1 is does not depend on the time variable that shows that the probability density does not depend on the time variable.

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Show that ${| ψ |}^{2} = {| ψ |}^{2}$ , with related as in Eq. 38-14. That is, show that the probability density does not depend on the time variable.

Short Answer

Step by step solution

Determine the concept and the formula

Determine the derivation as:

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Show that|ψ|2=|ψ|2 , with related as in Eq. 38-14. That is, show that the probability density does not depend on the time variable.

Short Answer

Step by step solution

Determine the concept and the formula

Determine the derivation as:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Radiation

Conservation of Energy and Momentum

Magnetism

Famous Physicists

Measurements

Fundamentals of Physics

Study anywhere. Anytime. Across all devices.

Show that ${| ψ |}^{2} = {| ψ |}^{2}$ , with related as in Eq. 38-14. That is, show that the probability density does not depend on the time variable.