Formulate the Schrödinger wave equation for the helium atom and find its approximate ground-state energy, neglecting electron-electron repulsion. 

The Schrödinger wave equation for the helium atom involves solving for the behavior of two electrons around a nucleus with two protons. The system is more complex than the hydrogen atom due to the presence of two electrons, each interacting with the nucleus and each other. In the simplest approach, neglecting the electron-electron repulsion, we can treat the two electrons as if each is independently attracted to the nucleus.

The time-independent Schrödinger equation for a two-electron system in the presence of a nucleus is:

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