Probability of finding a particle between a and b:

P_ab=

Heisenburg Uncertainty Principles:

h-bar/2=

≤ΔxΔp

≤ΔEΔt

≤ΔLΔΦ

≤ΔL_iΔL_j

deBroglie Wavelength:

λ=

f=

=h/p = h/(mu)

=E/h

Kinetic Energy Delivered to Electrons:

T_max=

=hf-φ

(φ = work "function")

Photoelectirc cutoff wavelength:

λ_c=

f_c=

=c/f_c=hc/φ

(f_c=φ/h)

Momentum of a photon (massless particle)

p=

=E/c

=hf/c

Expectation value:

=

=∫_-∞^∞ψ*xΨ

Kinetic Energy of a photoelectron:

T_max=

=eΔV_s

=hf_max

(e=charge of electron)

Allowed energy of an oscillator:

E=

=nhf

Peak of blackbody curve:

λ_maxT=

=2.898_E-3 mK

E=π²(h-bar)²/(2ma²)

E_n=(n+1/2)hf