QM 1 - vibrational motion

how are the energy levels of the harmonic oscillator spaced? why?

they are equally spaced

the steepness of the parabolic potential is just right

how do the atoms move in a diatomic molecule vibration?

the atoms move back and forth from their equilibrium positions

the distance between them is the equilibrium bond length of the molecule

motion is synchronised - atoms move closer together as the bond between is compressed and move further as the bond is stretched

how is a diatomic vibration thought of?

describe vibration as if it were a single particle oscillating

using reduced mass

show potential energy vs displacement parabola and describe it

how does it change with increasing k?

symmetrical

what is the relationship between ‘restoring’ force and displacement?

what does this mean?

negative sign means the force always acts to restore the system to equilibrium

when bond is stretched, the force pushes the atoms back

when compressed, it pulls the atoms away

what does it mean that the parabola is symmetric about x=0?

in vibration, stretching and compression are equally hard

potential energy increases in exactly the same way whether you displace the atoms to the left or right

what does the force constant mean?

quantifies the resistance to stretching and compression (displacement from equilibrium position)

what does a large force constant mean?

steep parabola

bond is stiff and hard to stretch/compress

what does a small force constant mean?

shallow parabola

bond is floppy and easy to deform