Equations, mathematical constructive interference

An approximate description of the MOs in H2 can be obtained by considering them as linear combinations of atomic orbitals (LCAOs). Each of the H atoms has one 1 atomic orbital let the two associated wavefunctions be ipi and In Section 1.6, we mentioned the importance of the signs of the wavefunctions with respect to their overlap during bond formation. The sign of the wavefunction associated with the I5 atomic orbital may be either + or —. Just as transverse waves interfere in a constructive (in-phase) or destructive (out-of-phase) manner, so too do orbitals. Mathematically, we represent the possible combinations of the two I5 atomic orbitals by equations 1.27 and 1.28, where N and N are the normalization factors. Whereas V mo is nn in-phase (bonding) interaction, ipuQ is an out-of-phase (antibonding) interaction. 

If we define the wavefunction in terms of the probability density, and it s the probability density that determines what we measure in the laboratory, then why do we need the wavefunction at all The wavefunction is a mathematical convenience that allows us not only to predict the properties of individual quantum states, but also to predict results that stem from combinations of quantum states. It is the wavefunction, not the probability density, that solves the Schrodinger equation, and—like a wave—the wavefunction can undergo constructive and destructive interference with other wavefunctions to accurately predict the resulting probability densities. 

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