# Subcontractor: Consider a two level system with Hamilatonian

**Question description**

Consider a two level system with Hamiltonian

H = E_0 |E_0> + E_1 |E_1>

where |E> is Dirac notation for a quantum state E with eigenstates

|E_0> = 1/sqr(2) ( |0> + |1> )

and

|E_1> = 1/sqr(2) ( |0> - |1>)

(a) Consider a quantum state which starts as |0> at t= 0. Compute the minimal amount of time it takes the system to reach the orthogonal state |1>. Express the answer in terms of the expectation value and/or the standard deviation of the energy.

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