A collection of undergraduate + graduate level physics problems to test LLMs with.

by Kyle Kabasares

Mathematical Physics

1. A physics problem has been reduced to calculating an integral of the form:

$$ \int_{0}^{\pi}\int_{0}^{\infty}\int_{0}^{\infty}\int_{0}^{\infty} \frac{dw dx dy dz}{1+w^2+x^2+y^2+z^2} $$

Part a:

1. Evaluate this integral and provide your answer as a closed-form solution.
2. Calculate the exact value of this integral numerically.

Solution

Classical Mechanics

Electromagnetism

Thermal Physics + Statistical Physics

Quantum Mechanics