Second order approximation in time independent perturbaton theory

[paweld]

Is there any physical reason why second order approximation to
ground state in time independent perturbation theory is always
negative. I know how to prove it mathematicly but I wonder
whether one may justify it using only physical arguments.

 

[faribataghavi]

because the energy of the tials functions are always more more than the ground state

 

[Entropia]

The second order approximation in time independent perturbation theory is always negative due to the nature of the perturbation itself. In this theory, a small perturbation is applied to a system that is initially in its ground state. This perturbation causes the system to deviate from its ground state, resulting in an energy shift. The second order approximation takes into account the second order effect of this perturbation on the energy of the system.

Physically, this second order effect results in a decrease in the energy of the system. This can be understood by considering the perturbation as a disturbance that disrupts the equilibrium of the system. As the system tries to return to its ground state, it must release energy in order to do so. This energy release is manifested in the negative value of the second order approximation.

Additionally, the perturbation itself is assumed to be small, which means that the second order effect is even smaller. This further justifies the negative value of the second order approximation, as it represents a small decrease in energy due to the perturbation.

In summary, the physical reason for the negative value of the second order approximation in time independent perturbation theory is due to the nature of the perturbation and its effect on the energy of the system.