def waveVector_deBroglie(momentum=1, units=SI):
""" deBroglie wave vector
arguments
---------
momentum: default = 1 [ mass velocity ], magnitude of momentum
units: default = SI
returns
-------
dictionary: keys('var', 'par', 'y' , 'f' , 'result' )
"""
var = sy.var('p hbar')
par = momentum, units['hbar']
y = p / hbar
return dic_result(var,par,y)
def probability_density(dic):
""" probability density psi* psi
requires psi function to have conjugate keyword argument
arguments
---------
dic: returned dictionary from desired psi function
returns
-------
dictionary: keys('var', 'par', 'y' , 'f' , 'result' )
"""
var = dic['var']
par = dic['par']
y1 = dic['y']
y = y1.conjugate() * y
return dic_result(var,par,y)
def wavelength_deBroglie(momentum=1, units=SI):
""" deBroglie wavelength
arguments
---------
momentum: default = 1 [ mass velocity ], magnitude of momentum
units: default = SI
returns
-------
dictionary: keys('var', 'par', 'y' , 'f' , 'result' )
"""
var = sy.var('h p')
par = units['h'], momentum
y = h / p
return dic_result(var,par,y)
def displacement_wein(temperature=1, units=SI):
""" wavelength of blackbody peak energy density
arguments
---------
temperature: default = 1 [K]
units: default = SI
returns
-------
dictionary: keys('var', 'par', 'y' , 'f' , 'result' )
"""
var = sy.var('h c k t')
par = units['h'], units['c'], units['k'], temperature
y = h * c / 4.9663 / k / t
return dic_result(var,par,y)
def wavelength_compton_shift(angle=0, units=SI):
""" shift in wavelength from compton scatter
arguments
---------
angle: default = 0 [degree], scattering angle
units: default = SI
returns
-------
dictionary: keys('var', 'par', 'y' , 'f' , 'result' )
"""
var = sy.var('h m_e c theta')
par = units['h'], units['m_e'], units['c'], np.deg2rad(angle)
y = h / (m_e * c) * ( 1 - sy.cos(theta) )
return dic_result(var,par,y)
def frequency_threshold(workFunction=1, units=eV):
""" threshold frequency of material
arguments
---------
workFunction: default = 1 [ energy ]
units: default = eV
returns
-------
dictionary: keys('var', 'par', 'y' , 'f' , 'result' )
"""
var = sy.var('W h')
par = workFunction, units['h']
y = W / h
return dic_result(var,par,y)
def intensity_blackbody(efficiency=1,temperature=1, units=SI):
""" power/area
parameters
----------
energy: default = 1 [ energy ]
temperature: default = 1 [ K ]
units: default SI
returns
-------
dictionary: keys('var', 'par', 'y' , 'f' , 'result' )
"""
var = sy.var('e sigma t')
par = efficiency, units['sigma'], temperature
y = e * sigma * t**4
return dic_result(var,par,y)
def energy_scattered_electron(photonEnergy=1, units=eV):
""" energy of scattered electron from compton scatter
arguments
---------
photonEnergy: default = 1 [ energy ], energy of photon before interaction
units: default = SI
returns
-------
dictionary: keys('var', 'par', 'y' , 'f' , 'result' )
"""
var = sy.var('m_e c E')
par = units['m_e'], units['c'], photonEnergy
m0 = m_e * c**2
y = m0 / ( (m0/E) + 2 )
return dic_result(var,par,y)
def potential_stopping(frequency=1,workFunction=1, units=eV):
""" stopping potential WRT frequency
arguments
---------
frequency: default = 1 [ 1 / time ]
workFunction: default = 1 [ energy ]
units: default = eV
returns
-------
dictionary: keys('var', 'par', 'y' , 'f' , 'result' )
"""
var = sy.var('h e nu W')
par = units['h'], units['e'], frequency, workFunction
y = (h/e) * nu - (W/e)
return dic_result(var,par,y)
def KE_ejected_electron(frequency=1,workFunction=1, units=eV):
""" kinetic energy of ejected photon
arguments
---------
frequency: default = 1 [ 1 / time ]
workFunction: default = 1 [ energy ]
units: default = eV
returns
-------
dictionary: keys('var', 'par', 'y' , 'f' , 'result' )
"""
var = sy.var('h nu W')
par = units['h'], frequency, workFunction
y = h*nu - W
return dic_result(var,par,y)
def distribution_planck_nu(frequency=1,temperature=1, units=SI,printA=False):
""" Planck energy density distribution WRT nu
arguments
---------
frequency: default = 1 [ 1 / time ]
temperature: default = 1 [ K ]
units: default SI
returns
-------
dictionary: keys('var', 'par', 'y' , 'f' , 'result' )
"""
var = sy.var('pi nu h c k t')
par = np.pi, frequency, units['h'], units['c'], units['k'], temperature
y = ( 8 * pi * nu**2 * h * nu ) / ( c**3 * (sy.exp(h*nu/k/t) - 1) )
return dic_result(var,par,y)
def distribution_planck_lambda(wavelength=1,temperature=1, units=SI,printA=False):
""" Planck energy density distribution WRT lambda
arguments
---------
wavelength: default = 1 [ length ]
temperature: default = 1 [ K ]
units: default = SI
returns
-------
dictionary: keys('var', 'par', 'y' , 'f' , 'result' )
"""
var = sy.var('pi h c l k t')
par = np.pi, units['h'], units['c'], wavelength, units['k'], temperature
y = ( 8 * pi * h * c ) / l**5 / ( sy.exp(h*c/l/k/t) - 1 )
return dic_result(var,par,y)
def energy_bohr_orbital(atomicZ=Z1,mass_n=mn1,num=1,units=eV):
""" find orbital energy of bohr-like atom
arguments
---------
atomicZ: default = 1, atomic number
mass_N: default = eV['m_n'], mass of nucleus
num: default = 1, orbital number
units: default = eV
returns
-------
dictionary: keys('var', 'par', 'y' , 'f' , 'result' )
"""
var = sy.var('Z me mn R n')
par = atomicZ, units['m_e'], mass_n, units['Rydberg'], num
y = - Z**2 / (1 + (me/mn)) * (R/n**2)
return dic_result(var,par,y)
def distribution_rayleigh_jean(frequency=1,temperature=1, units=SI):
""" Rayleigh Jean's energy density distribution
arguments
---------
frequency: default = 1 [ 1 / time ]
temperature: default = 1 [ K ]
units: default SI
returns
-------
dictionary: keys('var', 'par', 'y' , 'f' , 'result' )
"""
var = sy.var('pi nu c k t')
par = np.pi, frequency, units['c'], units['k'], temperature
y = ( 8 * pi * nu**2 * k * t ) / ( c**3 )
return dic_result(var,par,y)
def energy_bohr_photon(atomicZ=Z1,mass_n=mn1,num1=1,num2=2,units=eV):
""" energy of absorbed/emitted photon from bohr-like atom
arguments
---------
atomicZ: default = 1, atomic number
mass_N: default = eV['m_n'], mass of nucleus
num1: default = 1, initial orbital number
num2: default = 2, final orbital number
units: default = eV
returns
-------
dictionary: keys('var', 'par', 'y' , 'f' , 'result' )
"""
var = sy.var('R Z me mn m n')
par = units['Rydberg'], atomicZ, units['m_e'], mass_n, num2, num1
y = R * Z**2 / ( (me/mn) + 1) * ( 1/n**2 - 1/m**2 )
return dic_result(var,par,y)
def radius_bohrlike(atomicZ=Z1,mass_n=mn1,num=1,units=eV):
""" find radius of bohr-like atom
arguments
---------
atomicZ: default = 1, atomic number
mass_N: default = eV['m_n'], mass of nucleus
num: default = 1, orbital number
units: default = eV
returns
-------
dictionary: keys('var', 'par', 'y' , 'f' , 'result' )
"""
var = sy.var('me mn a0 Z n')
par = units['m_e'], mass_n, units['a_0'], atomicZ, num
y = (1 + me/mn) * (a0/Z) * n**2
return dic_result(var,par,y)
def uncertainty_heisenberg(uncertainty=1,symb=deltap, units=SI):
""" finds the uncertainty between two conjugate paired variables
arguments
---------
var: default = dp, uncertainty of known conjugate variable
units: default = SI
returns
-------
dictionary: keys('var', 'par', 'y' , 'f' , 'result' )
"""
var1 = sy.var(symb)
var2 = sy.var('hbar')
var = var1,var2
par = uncertainty,units['hbar']
y = var2 / var1
return dic_result(var,par,y)
def distribution_wein(a0=1,a1=1,frequency=1,temperature=1):
""" Wien's energy density distribution
arguments
---------
a1: default = 1, fitting parameter 1
a2: default = 1, fitting parameter 2
frequency: default = 1 [ 1 / time ]
temperature: default = 1 [K]
returns
-------
dictionary: keys('var', 'par', 'y' , 'f' , 'result' )
"""
var = sy.var('a:2 nu t')
par = a0, a1, frequency, temperature
y = var[0] * nu**3 * sy.exp( - var[1]*nu/t)
return dic_result(var,par,y)
def energy_photon_pair_production(k_electron=1,k_proton=1,k_nucleus=1,m_nucleus=1, units=eV):
"""
arguments
---------
k_electron: default = 1 [ energy ], kinetic energy of electron
k_proton: default = 1 [ energy ], kinetic energy of positron
k_nucleus: default = 1 [ energy ], kinetic energy of nucleus
m_nucleus: default = 1 [ mass ], mass of nucleus
units: default = eV
returns
-------
dictionary: keys('var', 'par', 'y' , 'f' , 'result' )
"""
var = sy.var('m_e c k_e k_p k_n m_n ')
par = units['m_e'], units['c'], k_electron, k_proton, k_nucleus, m_nucleus
y = (2 * m_e + m_n) * c**2 + k_e + k_p + k_n
return dic_result(var,par,y)