Schrodinger Equation: Kinetic Energy Impact?

[HarryDaniels]

I am sure you are all aware of the Schrödinger equation.

The Hamiltonian is included in this equations, which contains the Kinetic energy operator. When Schrödinger wrote thi he converted momentum to the unit imaginary number, the reduced Planck constant and the Delta operator.

My question is that this means that the Kinetic energy will be the same regardless of the characteristics of the quantum level particle. This does not make sense, surely the kinetic energy will affect the evolution of the state, due to the fact that it is energy.

Thanks to whoever clears this up for me.

-H

 

[ChmDudeCB]

I am sure you are all aware of the Schrödinger equation.

The Hamiltonian is included in this equations, which contains the Kinetic energy operator. When Schrödinger wrote thi he converted momentum to the unit imaginary number, the reduced Planck constant and the Delta operator.

My question is that this means that the Kinetic energy will be the same regardless of the characteristics of the quantum level particle. This does not make sense, surely the kinetic energy will affect the evolution of the state, due to the fact that it is energy.

Thanks to whoever clears this up for me.

-H

Can you clarify your question?

The Hamiltonian is E = Ke + V where Ke is the kinetic component and V is the potential component.

Kinetic energy is related to the angular momentum and the momentum at any given point is the curvature of the particle at that point which changes with quantum state.

 

[tom.stoer]

I am not sure if you are aware of the relation between the classical Hamilton function and the Hamilton operator.

In both classical and quantum mechanics we can write

$$H = E_\text{kin} + E_\text{pot}$$

The kinetic energy is expressed via the momentum as

$$E_\text{kin} = \frac{p^2}{2m}$$

In quantum mechanics you replace

$$p \to \hat{p} = -i\partial_x$$

and therefore you convert the Hamilton function in an operator acting on quantum states or wave functions.