# Is wave function a probability function of time?

Wave function ψ(x,t) is a fuction of probability which depends on time example
Ψ(x,t)=1/(c-v)t Lets suppose its a function of probability
It depends on time and it affects space.
Is this is a definition of wave function ?
(I know wave function squuared gives probability but I am not asking that )

Nugatory
Mentor
The wave function has to be a solution of Schrodinger's equation, and that restricts it to one particular form of time dependency. The ##\Psi## that you propose above won't work, as you'll see if you try plugging it into Schrodinger's equation.

In elementary (meaning before the Hilbert space formalism is introduced) quantum mechanics the wave function can be written as a function of position and time, or as a function of momentum and time. You can transform between the two forms; the former is used to calculate the probability of finding the particle at a given position at a given time and the latter to calculate the probability of finding the particle with a given momentum at a given time.

bhobba
If i remember well all the wavefunctions must obey to the conservation of probability:
##\nabla j(x,t)+\frac{\partial \rho (x,t)}{\partial t}=0##
where:
##j(x,t)=-\frac{i \hbar}{2m}(\psi * \nabla \psi - \psi \nabla \psi*)##
##\rho(x,t)=|\psi|^2##

Lets suppose there a space-time function (simple coordinate function, depends time) Ψ(t)=2t
Lets make a problem; The probability of finding particle on the line between zero and t intervals
Line lenght 0 and 2t than whats the probabilty of finding particle between this intervels ?
Can we solve it useing wavefunction

vanhees71
Gold Member
2021 Award
That's not a valid wave function either, because it must be square integrable (also be aware that we discuss only non-relativistic single-particle quantum theory here).

Can I turn it a wavefunction someway but same logic

Nugatory
Mentor
Can I turn it a wavefunction someway but same logic

No. You have to write down the Hamiltonian of the system, then you have to insert that Hamiltonian into Schrodinger's equation and solve for the wavefunction.

If I do that ,can I find the right answer ? I want to be sure sorry but thank you