First prove A and B to be Hermitian Operators, and then prove (A+B)^2 to be hermitian...

First prove A and B to be Hermitian Operators, and then prove (A+B)^2 to be hermitian operators.

Expert Solution

genius_generous answered 2 years ago

2. (a). Prove that the sum of the two projection operators is not a projection operator,...

2. (a). Prove that the sum of the two projection operators is not a projection operator, unless the multiplication of the two projection operators produces a zero value. (b). Prove that the result of the multiplication of two projection operators is not a projection operator, unless the two projection operators are hermitian.

Prove that if A and B are 2x2 matrices, then (A + B)^(2) = A^(2) +...

Prove that if A and B are 2x2 matrices, then (A + B)^(2) = A^(2) + AB + BA + B^(2). Hint: Write out 2x2 matrices for A and B using variable entries in each location and perform the operations on either side of the equation to determine whether the two sides are equivalent.

Prove that for a wave function to be a simultaneous eigenfunction of two operators A and...

Prove that for a wave function to be a simultaneous eigenfunction of two operators A and C, the operators must commute.

4. Prove that if there are two operators A, ˆ Bˆ, such that their commutator [A,...

4. Prove that if there are two operators A, ˆ Bˆ, such that their commutator [A, ˆ Bˆ] = λ where λ is a constant. Show that (6 points) exp[μ(Aˆ + Bˆ)] = exp(μAˆ) exp(μBˆ) exp(−μ 2λ/2) where given an operator Xˆ; exp(tXˆ) = 1 + tXˆ + 1 2 t 2Xˆ 2 + ... + 1 n! t nXˆ n + ... (the usual exponential series implemented for operators).

Not all operators are commutative, namely, ab = ba. Consider functions under the operators addition, subtraction,...

Not all operators are commutative, namely, a*b = b*a. Consider functions under the operators addition, subtraction, multiplication, division, and composition. Pick two of the functions and use a grapher (like Desmos) to graph the functions under the operators. If the functions are commutative under the operator, the graphs should be identical (overlap everywhere) when you change the order in which the functions are entered with the operator. Determine which operators seem to the commutative and which operators seem not to...

Prove that if (6; a) = (6; b) = 1, then 24 | (a^2 - b^2).

prove that positive operators have unique positive square root

2. (a) Prove that U45 is generated by the set {14,28}. (b) Prove that the additive...

2. (a) Prove that U45 is generated by the set {14,28}. (b) Prove that the additive group Z×Z is generated by the set S={(3,1),(−2,−1),(4,3)}. Please be thorough step by step with details, please.

2. Prove the following properties. (b) Prove that x + ¯ xy = x + y.

2. Prove the following properties.(b) Prove that x + ¯ xy = x + y.3. Consider the following Boolean function: F = x¯ y + xy¯ z + xyz(a) Draw a circuit diagram to obtain the output F. (b) Use the Boolean algebra theorems to simplify the output function F into the minimum number of input literals.

a. Prove that y=sin(x) is a subspace of R^2 b. Prove that a set of 2x2...

a. Prove that y=sin(x) is a subspace of R^2 b. Prove that a set of 2x2 non invertible matrices a subspace of all 2x2 matrices

Question