Lowest-order correction for the bendulum

[eman2009]

what is the lowest-order correction to the ground state for the pendulum with small angle?

 

[per.sundqvist]

[tex]cos(x)=1-x^2/2!+x^4/4!-...[/tex]
[tex]\delta E\propto<\Psi_0\mid x^4\mid\Psi_0>[/tex]

 

[Entropia]

The lowest-order correction for the pendulum refers to the first correction term in the perturbation expansion of the system. In the case of the pendulum with small angle, this correction takes into account the deviation from the idealized simple harmonic motion due to the nonlinearity of the pendulum's motion.

The lowest-order correction to the ground state for the pendulum with small angle can be calculated using the first-order perturbation theory. This involves considering the effect of the nonlinear term in the pendulum's potential energy on the ground state energy.

The result of this calculation is a small correction to the ground state energy, which takes into account the deviation from the idealized simple harmonic motion. This correction is typically expressed as a small fraction of the ground state energy and is a measure of the nonlinearity of the system.

In practical applications, this correction can be important in accurately predicting the behavior of the pendulum, especially for larger amplitudes or longer time periods. Therefore, it is crucial for scientists to consider the lowest-order correction when studying the dynamics of the pendulum.