The Van der Waals potential is fundamental to describing intermolecular interactions, yet the Schrödinger equation for this potential lacks a general analytical solution. This work introduces a variational Physics-Informed Neural Network (PINN) approach to determine the ground state energy and wavefunction of a particle in a combined Van der Waals and harmonic trap potential. By framing the problem within the Rayleigh-Ritz variational principle, the neural network is trained to minimize the expectation value of the Hamiltonian, thereby finding the ground state without needing to solve the differential equation directly as a residual problem. We investigate the ground state energy as a function of the harmonic trap frequency ω, demonstrating that the PINN results correctly interpolate between the weakly-trapped (Van der Waals dominated) and strongly-trapped (harmonic oscillator dominated) regimes. The model’s predictions align perfectly with theoretical limits, validating its accuracy. This study highlights the capability of variational PINNs to tackle complex quantum systems where traditional analytical methods are intractable.