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- For a particle, the unperturbed states are with the allowed (dimensionless) energies = 0, +1, +2, .... If we introduce the perturbation Hamiltonian Â' such of n², where n = that: 0.5 0.2 0 for k=1 and g = -1 for k=g = 0 0.3 ) Find the (dimensionless) first order correction to the ground state energy for k= g = 1 for k=g = −1 (Y|A|) =I'm new to Dirac notation, I know the basics of bra and kets. Howewer I can't understand this. Could you explain how the upper expresion equals below expresion. What does <x^2>0 mean? ( This is 7.36 exersixe in quantum mechanics book )Write Dirac’s equation for a free particle. Find the form of the probability density and the probability current density in Dirac’s formalism.