# How can we write the wave function in quantum mechanics?

In quantum mechanics, while writing the wave functions we can take a product of the spatial and the spin parts.But what does it means? What is the meaning of the spatial wave function and the spin wave function?

• Can you please provide the expressions for the wavefunction? Nov 12 '13 at 12:09
• Welcome to Chemistry.SE! May I ask what background you have in Quantum Mechanics? Are you familiar with Hilbert spaces and Tensor products? Your state of knowledge will determine the kind of answer you get, since this question could require some rather involved mathematical concepts in order to answer it completely. Nov 12 '13 at 18:41
• I have quantum mechanics course in my master science ..... I don't that much Hilbert spaces and Tensor products...... Apr 20 '15 at 17:14

Within the Born-Oppenheimer approximation, we 'index' all the values required to describe where an electron is. This includes the spatial coordinates, ($\textbf{r}$), and the spin coordinate, $\omega$. Electrons are characterized by their spin ($\uparrow$ vs. $\downarrow$). Another way to think about it is this. The quantum numbers are used to describe everything we need to know about 'where' an electron is ($n$, $l$, $m_l$, $m_s$). The spatial coordinates (e.g. Cartesian coordinates) take care of the first 3 quantum numbers. We need the fourth coordinate to characterize $m_s$.