Show that the operator $\hat{p}^{\prime}$ obtained by applying a translation to the operator $\hat{p}$ is $\hat{p}^{\prime}=\hat{T}^{\dagger} \hat{p} \hat{T}=\hat{p}$.

What is the instanceof operator of a class?

Which of the following is not a comparison operator? * <> = << <=

Unary operator on X: function from X to X

What does the assignment of township lots reveal about values of Americans at this time?

What is the purpose of the & operator in a macro definition?

Binary operator on X: function from X x X to X

(Operator Overloading in Templates) Write a simple function template for predicate function is Equal To that compares its two arguments of the same type with the equality operator (==) and returns true if they are equal and false otherwise. Use this function template in a program that calls isEqualTo only with a variety of fundamental types. Now write a separate version of the program that calls isEqualTo with a user-defined class type, but does not overload the equality operator. What happens when you attempt to run this program? Now overload the equality operator (with the operator function) operator==. Now what happens when you attempt to run this program?

Briefly describe how the | | operator works.

An anti-hermitian (or skew-hermitian) operator is equal to minus its hermitian conjugate: $\hat{Q}^{\dagger}=-\hat{Q}$. (a) Show that the expectation value of an anti-hermitian operator is imaginary. (b) Show that the eigenvalues of an anti-hermitian operator are imaginary. (c) Show that the eigenvectors of an anti-hermitian operator belonging distinct eigenvalues are orthogonal. (d) Show that the commutator of two hermitian operators is anti-hermitian. How about the commutator of two anti-hermitian operators? (e) Show that any operator $\hat{Q}$ can be written as a sum of a hermitian operator $\hat{A}$ and an anti-hermitian operator $\hat{B}$, and give expressions for $\hat{A}$ and $\hat{B}$ in terms of $\hat{Q}$ and its adjoint $\hat{Q}^{\dagger}$.

T F The & operator dereferences a pointer.

Briefly describe how the or operator works

What is the purpose of the ! Operator in a macro definition?

Consider the linear operator of left multiplication by an $m \times m$ matrix A on the space $F^{m \times m} \text { of all } m \times m$ matrices. Determine the trace and the determinant of this operator.