We report an educational tool for the upper level undergraduate quantum chemistry or quantum physics course that uses a symbolic approach via the PySyComp Python library. The tool covers both time-independent and time-dependent quantum chemistry, with the latter rarely considered in the foundations course due to topic complexity. We use quantized Hamiltonian dynamics (QHD) that provides a simple extension of classical dynamics and captures key quantum effects. The PySyComp library can compute various concepts regarding the fundamental postulates of quantum mechanics, including normalized wave functions, expectation values, and commutators, which are at the core of solving the Heisenberg equations of motion. It provides a tool for students to experiment with simple models and explore the key quantum concepts, such as zero-point energy, tunneling, and decoherence.