From the post "Bouncy Balls, Sticky Balls, Transfer Of Momentum",
\(\Delta\,p=\cfrac{2}{c}\int ^{ x_{z} }_{a }{ \psi } d\, x\)
for a particle of radius \(a\), and \(a=0\) is possible.
And from the post "To Assume Or Not To Assume",
\(m_{ \rho \, p }c^{ 2 }=m_{ \rho }c^{ 2 }-\int _{ 0 }^{ x_{ a} }{ \psi } dx\) --- (*)
In the case when, \(a=0\),
\(m_{ \rho }c^{ 2 }=\int _{ 0 }^{ x_{ a} }{ \psi } dx=2\int _{ 0 }^{ x_{ z} }{ \psi } dx\)
therefore,
\(\Delta\,p=\cfrac{1}{c}\int ^{ x_{z} }_{0 }{ \psi } d\, x=m_{ \rho }c\)
From the posts "Size Of Basic Particle From Its Spectrum" and "Not All Integer But Half Has A Place",
\(f=n\cfrac{c}{2\pi a_\psi}\)
And we have,
\(\Delta\,p=2\pi a_\psi m_{ \rho }\cfrac{f}{n}=2\pi a_\psi m_{ \rho } c\cfrac{1}{n\lambda_n}\)
where around \(2\pi a_\psi\), \(n=1,2,3...\) wavelengths are packed.
\(\Delta\,p=\cfrac{h_\rho}{\lambda_n}\)
where \(h_\rho=2\pi a_\psi m_{ \rho }c\cfrac{1}{n}\), \(n=1,2,3...\)
Momentum decreases with \(n\). When \(n=1\) we have Louis de Broglie postulation that all particles with momentum have a wavelength,
\(\Delta\,p=\cfrac{h_\rho}{\lambda}\),
where \(h_\rho=2\pi a_\psi m_{ \rho }c\)
In this general case however, all particles have momentum that is the result of a change in \(\psi\) and in the case when the particle is fully manifested as \(\psi\), and all of \(\psi\) is "converted" to momentum,
\(\Delta\,p=m_{ \rho }c\)
is a constant. In the case where the particle is not completely \(\psi\), from relationship (*),
\(m_{ \rho \, p }c^{ 2 }+\int _{ 0 }^{ x_{ a} }{ \psi } dx=m_{ \rho }c^{ 2 }\)
\(m_{ \rho \, p }c+\cfrac{2}{c}\int _{ 0 }^{ x_{ z} }{ \psi } dx=m_{ \rho }c\)
\(m_{ \rho \, p }c+\Delta\,p=m_{ \rho }c\)
the total momentum of the particle is still,
\(p_\rho=p_m+\Delta\,p=m_{ \rho }c\) a constant
where \(p_m=m_{ \rho \, p }c\) is the momentum of the particle due to its mass, and \(\Delta\,p\) is the momentum of the particle due to a change in its \(\psi\).
