Wave function description and Schrödinger's equation

[AleksanderPhy]

Hello I am not professional at physics and new on this forum so don't be angry when I make mistakes
So my question is about wave function so is it right that ψ=Asin(kx)+Bcos(kx) where A and B are constants, k is a some constant k=√2mE/ħ^2 and x is cordinate so when we give A and B value and do little bit math work then we got number. My question is can we describe wave function on some single point ? And can you guys give my steps for solving that beadiful equation on free particle.

 

[hokhani]

My question is can we describe wave function on some single point ?

Wave function at each point gives the probability of presence there and wave function has value at all points. If the particle is confined within a limited region the wave function is zero out of that region.

 

[AleksanderPhy]

Thank you very much

 

[jtbell]

Wave function at each point gives the probability of presence

Actually, it is $\psi^*\psi$ (that is, $\psi^*$ (the complex conjugate of $\psi$) times $\psi$) that gives the probability density. In this case, $\psi$ is real, not complex, so $\psi^*\psi = \psi^2$.

And can you guys give my steps for solving that beadiful equation on free particle.

A Google search for "solution of schrodinger equation for free particle" finds many web pages which give the derivation. Choose one and study it. If you don't understand some of the steps, tell us which ones and someone will probably help you.

 

[AleksanderPhy]

Thank you two Your tips helped me a loot