introduction to quantum mechanics

Key points

• Louis de Broglie proposed that all particles could be treated as matter waves with a wavelength $\lambda$λlambda, given by the following equation:

$\lambda=\dfrac{h}{mv}$λ=​mv​​h​​lambda, equals, start fraction, h, divided by, m, v, end fraction

• Erwin Schrödinger proposed the quantum mechanical model of the atom, which treats electrons as matter waves.
• Schrödinger's equation, $\hat{H}\psi=E\psi$​H​^​​ψ=Eψ, can be solved to yield a series of wave function $\psi$ψ, each of which is associated with an electron binding energy, $E$EE.
• The square of the wave function, $\psi^2$ψ​2​​, represents the probability of finding an electron in a given region within the atom.
• An atomic orbital is defined as the region within an atom that encloses where the electron is likely to be 90% of the time.
• The Heisenberg uncertainty principle states that we can't know both the energy and position of an electron. Therefore, as we learn more about the electron's position, we know less about its energy, and vice versa.
• Electrons have an intrinsic property called spin, and an electron can have one of two possible spin values: spin-up or spin-down.
• Any two electrons occupying the same orbital must have opposite spins