Let us consider two wavefunctions |1) and |2) that only depend on an angle alpha

Question

Let us consider two wavefunctions |1) and |2) that only depend on an angle alpha (alpha|1) = A cos alpha and (alpha|2) = A sin alpha Where alpha elementof [0, 2pi]. Find the normalization constant A. Calculate the matrix R for the operator had R = i d/d alpha, within the basis |1) and |2). Find the eigenvalues and eigenvectors of R. Express the eigenfunctions as a function of alpha. Express the following exponent e^-iR alpha in a single 2 times 2 matrix. Calculate the effect of e^-iR alpha on an arbitrary wavefunction |psi) = cos alpha_0|1) + sin alpha_0|2). How can we interpret this operation?

Explanation / Answer

Ans-

The int(expression, x) calling sequence computes an indefinite integral of the expression with respect to the variable x.Note: No constant of integration appears in the result.

The int(expression, x = a..b) calling sequence computes the definite integral of the expression with respect to the variablex on the interval from a to b.

The int(expression, [ranges or variables]) calling sequence computes the iterated definite integral of the expression with respect to the variables or ranges in the list in the order they appear in the list. Note: The notation int(expression, [x = a..b, y = c..d]) is equivalent to int(int(expression, x = a..b), y = c..d) except that the single call to int accounts for the range of the outer variables (via assumptions) when computing the integration with respect to the inner variables.

You can enter the command int using either the 1-D or 2-D calling sequence. For example, int(f,x) is equivalent to fdx.

If any of the integration limits of a definite integral are floating-point numbers (e.g. 0.0, 1e5 or an expression that evaluates to a float, such as exp(-0.1)), then int computes the integral using numerical methods if possible (see evalf/int). Symbolic integration will be used if the limits are not floating-point numbers unless the numeric=true option is given.

If Maple cannot find a closed form expression for the integral (or the floating-point value for definite integrals with float limits), the function call is returned.

Note: For information on the inert function, Int, see int/details.

The int(expression, x) calling sequence computes an indefinite integral of the expression with respect to the variable x.Note: No constant of integration appears in the result.

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.