Examples Ground state

initial wave functions first 4 states of one-dimensional particle in box



the wave function of ground state of particle in one-dimensional half-period sine wave goes 0 @ 2 edges of well. energy of particle given







h

2



n

2




8
m

l

2







{\displaystyle {\frac {h^{2}n^{2}}{8ml^{2}}}}

, h planck constant, m mass of particle, n energy state (n = 1 corresponds ground-state energy), , l width of well.
the wave function of ground state of hydrogen atom spherically-symmetric distribution centred on nucleus, largest @ center , reduces exponentially @ larger distances. electron found @ distance nucleus equal bohr radius. function known 1s atomic orbital. hydrogen (h), electron in ground state has energy 3017782103997768000♠−13.6 ev, relative ionization threshold. in other words, 13.6 ev energy input required electron no longer bound atom.
the exact definition of 1 second of time since 1997 has been duration of 9,192,631,770 periods of radiation corresponding transition between 2 hyperfine levels of ground state of caesium-133 atom @ rest @ temperature of 0 k.




^ unit of time (second) . si brochure. international bureau of weights , measures. retrieved 2013-12-22.