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review derivation: Compton's equation for scattering

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Index Inference Rule Input latex Feeds latex Output latex step validity dimension check unit check notes
2 declare initial expr
  1. 8257621077; locally 2840008:
    \(\vec{p}_{\rm before} = \vec{p}_{1}\)
    \(pdg_{1302} = pdg_{6029}\)
no validation is available for declarations 8257621077:
8257621077:
5 substitute LHS of expr 1 into expr 2
  1. 3951205425; locally 2491904:
    \(\vec{p}_{\rm after} = \vec{p}_{1}\)
    \(pdg_{5493} = pdg_{6029}\)
  2. 8311458118; locally 1209604:
    \(\vec{p}_{\rm after} = \vec{p}_{2}+\vec{p}_{electron}\)
    \(pdg_{5493} = pdg_{2097} + pdg_{4299}\)
  1. 8139187332; locally 5610925:
    \(\vec{p}_{1} = \vec{p}_{2}+\vec{p}_{electron}\)
    \(pdg_{6029} = pdg_{2097} + pdg_{4299}\)
valid 3951205425:
8311458118:
8139187332:
3951205425:
8311458118:
8139187332:
7 swap LHS with RHS
  1. 5530148480; locally 4068150:
    \(\vec{p}_{1}-\vec{p}_{2} = \vec{p}_{electron}\)
    \(- pdg_{2097} + pdg_{6029} = pdg_{4299}\)
  1. 7917051060; locally 4200334:
    \(\vec{p}_{electron} = \vec{p}_{1}-\vec{p}_{2}\)
    \(pdg_{4299} = - pdg_{2097} + pdg_{6029}\)
valid 5530148480:
7917051060:
5530148480:
7917051060:
3 declare initial expr
  1. 8311458118; locally 1209604:
    \(\vec{p}_{\rm after} = \vec{p}_{2}+\vec{p}_{electron}\)
    \(pdg_{5493} = pdg_{2097} + pdg_{4299}\)
no validation is available for declarations 8311458118:
8311458118:
8 multiply expr 1 by expr 2
  1. 7917051060; locally 4200334:
    \(\vec{p}_{electron} = \vec{p}_{1}-\vec{p}_{2}\)
    \(pdg_{4299} = - pdg_{2097} + pdg_{6029}\)
  2. 7917051060; locally 4200334:
    \(\vec{p}_{electron} = \vec{p}_{1}-\vec{p}_{2}\)
    \(pdg_{4299} = - pdg_{2097} + pdg_{6029}\)
  1. 6742123016; locally 4218805:
    \(\vec{p}_{electron}\cdot\vec{p}_{electron} = ( \vec{p}_{1}\cdot\vec{p}_{1})+( \vec{p}_{2}\cdot\vec{p}_{2})-2( \vec{p}_{1}\cdot\vec{p}_{2})\)
    \(pdg_{4299}\)
Nothing to split 7917051060:
7917051060:
6742123016:
7917051060:
7917051060:
6742123016:
6 subtract X from both sides
  1. 8139187332; locally 5610925:
    \(\vec{p}_{1} = \vec{p}_{2}+\vec{p}_{electron}\)
    \(pdg_{6029} = pdg_{2097} + pdg_{4299}\)
  1. 0002338514:
    \(\vec{p}_{2}\)
    \(pdg_{2097}\)
  1. 5530148480; locally 4068150:
    \(\vec{p}_{1}-\vec{p}_{2} = \vec{p}_{electron}\)
    \(- pdg_{2097} + pdg_{6029} = pdg_{4299}\)
valid 8139187332:
5530148480:
8139187332:
5530148480:
4 substitute LHS of expr 1 into expr 2
  1. 8257621077; locally 2840008:
    \(\vec{p}_{\rm before} = \vec{p}_{1}\)
    \(pdg_{1302} = pdg_{6029}\)
  2. 1638282134; locally 4978059:
    \(\vec{p}_{\rm before} = \vec{p}_{\rm after}\)
    \(pdg_{1302} = pdg_{5493}\)
  1. 3951205425; locally 2491904:
    \(\vec{p}_{\rm after} = \vec{p}_{1}\)
    \(pdg_{5493} = pdg_{6029}\)
LHS diff is -pdg5493 + pdg6029 RHS diff is pdg5493 - pdg6029 8257621077:
1638282134: dimensions are consistent
3951205425:
8257621077:
1638282134: N/A
3951205425:
1 declare initial expr
  1. 1638282134; locally 4978059:
    \(\vec{p}_{\rm before} = \vec{p}_{\rm after}\)
    \(pdg_{1302} = pdg_{5493}\)
no validation is available for declarations 1638282134: dimensions are consistent
1638282134: N/A
Physics Derivation Graph: Steps for Compton's equation for scattering

Symbols for this derivation

See also all 212 symbols
symbol ID category latex scope dimension name value Used in derivations references
2097 variable \vec{p}_2
\(\vec{p}_2\)
real
  • length: 1
  • time: -1
  • mass: 1
momentum 2 5
6029 variable \vec{p}_1
\(\vec{p}_1\)
real
  • length: 1
  • time: -1
  • mass: 1
momentum 1 5
5493 variable \vec{p}_{\rm after}
\(\vec{p}_{\rm after}\)
real
  • length: 1
  • time: -1
  • mass: 1
momentum after collision 3
1302 variable \vec{p}_{\rm before}
\(\vec{p}_{\rm before}\)
real
  • length: 1
  • time: -1
  • mass: 1
momentum before collision 2
4299 variable \vec{p}_{\rm electron}
\(\vec{p}_{\rm electron}\)
real
  • length: 1
  • time: -1
  • mass: 1
momentum of electron 5
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