Is this interpretation of the change in mass of a wave function correct?
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I was interested in how a wave function of a single particle in no potential behaves if it was to lose mass.
ψ=Cei2mE√x/ℏψ=Cei2mEx/ℏ
So I took the derivative with respect to the mass, and a few algebra steps later of noting that all the energy is kinetic energy I could write the following in terms of the velocity.
∂ψ∂m=ixv2ψ∂ψ∂m=ixv2ψ
I was curious, when is the mass at a maximum or minimum? That should be when this is 0, and since ψψ is a complex exponential it is nonzero for all values and we end up with this equation:
0=x∗v0=x∗v
So the mass is at a maximum when x=0x=0 or v=0v=0, which seems to say when looking at a particle that is either localized in one place or when it is not moving relative to the reference frame...
Is this interpretation in any way correct? Regardless of the physical observation that particles may not continuously change mass, is this consistent with the mathematical model
ψ=Cei2mE√x/ℏψ=Cei2mEx/ℏ
So I took the derivative with respect to the mass, and a few algebra steps later of noting that all the energy is kinetic energy I could write the following in terms of the velocity.
∂ψ∂m=ixv2ψ∂ψ∂m=ixv2ψ
I was curious, when is the mass at a maximum or minimum? That should be when this is 0, and since ψψ is a complex exponential it is nonzero for all values and we end up with this equation:
0=x∗v0=x∗v
So the mass is at a maximum when x=0x=0 or v=0v=0, which seems to say when looking at a particle that is either localized in one place or when it is not moving relative to the reference frame...
Is this interpretation in any way correct? Regardless of the physical observation that particles may not continuously change mass, is this consistent with the mathematical model
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This is the equation for a ( non-relativistic) particle of mass m moving ... This interpretation requires a normalized wavefunction, namely, the ... does not change in
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