Energy Operator

 Energy Operator

Energy Operator :

 

- In Quantum Mechanics, Energy Is Defined In Terms Of The

  Energy Operator

- In Quantum Mechanics, The Energy Operator Is A Mathematical

  Operator Associated With Measuring The Energy Of A Quantum

  System.

- It Is Represented By The Symbol "E" Or "Ê" And Is Often

  Referred To As The Hamiltonian Operator.

 

- ψ(x,t) = A^ei(kx-ωt)

  (kx-ωt) Term Multiplied & Divide By ħ

- ψ(x,t) = Aei(kx-ωt)

              = Ae^{i(ħkx-ħωt)/ħ}

              = Ae^i(Px-Et)/ħ........(1)    (ħk=P & ħω=E)

- Derivation To Eqaution (1) With Respect To Time

- ∂Ψ/∂t = Ae^i(Px-Et)/ħ - iE/ħ......(2)

-put value of  ψ(x,t) = Ae^i(Px-Et)/ħ in eqaution (2)

- ∂Ψ/∂t = - iE/ħ ψ

  ∂/∂t = - iE/ħ 

  E = - ħ/i  ∂/∂t......(3)

Eqaution (3) Right Hand Side Multiplied & Divide By i

- E = - ħ/i  ∂/∂t

    = - iħ/i² ∂/∂t

- Ê = iħ ∂/∂t   (i²=-1)

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