Homework

1.

Modify the Fortran code example 1 to calculate the configuration integral, and the average potential energy of the one-dimensional anharmonic oscillator with the potential U(x)=-x²+x⁴ at T=0.1 to 1.0, with the increment of 0.1. Perform calculations with 10, 100, 1000, 10000, and 100000 steps and show how does the error decrease with the number of steps. Plot the running average as the function of the number of cycles.

2.

Modify the Fortran code example 2 to calculate the average potential energy and coordinate, and their mean squared deviations, of the one-dimensional anharmonic oscillator with the potential U(x)=-x²+x⁴ at T=0.1 to 1.0, with the increment of 0.1. Perform calculations with 10, 100, 1000, 10000, and 100000 steps and show how does the error decrease with the number of steps. Compare to the previous example.