Q69E does the wave function have a we... [FREE SOLUTION]

Chapter 5: Q69E (page 191)

does the wave function have a well-defined $蠄 (x) = A (e^{i k x} + e^{- i k x})$ momentum? Explain.

Short Answer

Expert verified

The constant in the front multiplies the initial function and two opposing moving plane waves are added, so the momentum is not clearly defined.

Step by step solution

Identification of given data

The wave function is $蠄 (x, t) = A (e^{i k x} + e^{- i k x}) .$

Concept/significance of Eigenvector

The eigenvectors of a linear transformation are those vectors where the transformation only modifies the magnitude of the vectors and not the angle. The "eigenvalue" of vectors refers to the ratio by which they differ from the original, and the vectors it works with are referred to as the "eigenvectors" corresponding to the eigenvalue.

Determination ofthe wave function has well-defined momentum:

The momentum operator is:

$\hat{p} 蠄 (x, t) = - i 鈩� \frac{鈭�}{鈭� x} 蠄 (x, t) .$

Replace the value of the wave function in the above equation.

$\begin{array}{rcl} \hat{p} 蠄 (x, t) & = & - i 鈩� \frac{鈭�}{鈭� x} A (e^{i k x} + e^{- i k x}) \\ = & - i 鈩� A (i k e^{i k x} - i k e^{- i k x}) \\ = & - i^{2} 鈩� k A (e^{i k x} - e^{- i k x}) \\ = & 鈩� k A (e^{i k x} - e^{- i k x}) . \end{array}$

Hence, the constant in the front multiplies the initial functionand two opposing moving plane waves are added, so the momentum is not clearly defined.

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91影视

does the wave function have a well-defined $蠄 (x) = A (e^{i k x} + e^{- i k x})$ momentum? Explain.

Short Answer

Step by step solution

Identification of given data

Concept/significance of Eigenvector

Determination ofthe wave function has well-defined momentum:

One App. One Place for Learning.

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91影视

does the wave function have a well-defined 蠄(x)=A(eikx+e-ikx)momentum? Explain.

Short Answer

Step by step solution

Identification of given data

Concept/significance of Eigenvector

Determination ofthe wave function has well-defined momentum:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Torque and Rotational Motion

Fluids

Waves Physics

Dynamics

Radiation

Oscillations

Study anywhere. Anytime. Across all devices.

does the wave function have a well-defined $蠄 (x) = A (e^{i k x} + e^{- i k x})$ momentum? Explain.