Prove that, -2=kT2Cv, using the canonical ensemble in quantum statistical mechanics,
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Prove that, <H2>-<H>2=kT2Cv, using the canonical ensemble in
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- Solve the following.The coherent states for the one-dimensional harmonic oscillator are defined as eigenstates of the operatorof annihilation a (which is non-Hermitian):a |λ⟩ = λ |λ⟩ (1)where λ is a complex number in general. a)prove that is a normalized consistent state. b)Show that the above state satisfies the minimum uncertainty relation, i.e., show thatIt's a quantum mechanics question.
- a) Show explicitly (by calculation) that the <p> = <p>* is fulfilled for the expectation value of themomentum. b) The three expressions xp, px and (xp+px)/2 are equivalent in classical mechanics.Show that for corresponding quantum mechanical operators in the orders shown, that <Q> = <Q>* isfulfilled by one of these operators, but not by the other two.Need help with the following statistical thermodynamics problem!Using the eigenvectors of the quantum harmonic oscillator Hamiltonian, i.e., n), find the matrix element (6|X² P|7).
- 6A qubit is in state |) = o|0) +₁|1) at time t = 0. It then evolves according to the Schrödinger equation with the Hamiltonian Ĥ defined by its action on the basis vectors: Ĥ0) = 0|0) and Ĥ|1) = E|1), where E is a constant with units of energy. a) Solve for the state of the qubit at time t. b) Find the probability to observe the qubit in state 0 at time t. Explain the result by referring to the way that the time-evolution transforms the Bloch sphere.I need the answer as soon as possible