Reshma
- 749
- 6
This one is from Liboff(p6.8)
Given the wavefunction:
\psi(x, t) = A exp[i(ax - bt)]
What is the Potential field V(x) in which the particle is moving?
If the momentum of the particle is measured, what value is found(in terms of a & b)?
If the energy is measured, what value is found?
My Work:
\psi(x, t) = A exp[i(ax - bt)]
I took the partial derivatives wrt to t and x:
\frac{\partial \psi}{\partial t} = -(ib)\psi
\frac{\partial^2 \psi}{\partial x^2} = -a^2\psi
Time dependent Schrodinger's equation is:
i\hbar \frac{\partial \psi}{\partial t} = -\frac{\hbar^2}{2m}\frac{\partial^2 \psi}{\partial x^2} + V(x)\psi
Substituting the above values in this equation:
\hbar b \psi = \frac{\hbar^2 a^2}{2m}\psi + V(x)\psi
Dividing throughout by \psi and rearranging, I get the potential field as:
V(x) = \hbar\left(b - \frac{\hbar a^2}{2m}\right)
Am I going right? Before I can proceed furthur...
Given the wavefunction:
\psi(x, t) = A exp[i(ax - bt)]
What is the Potential field V(x) in which the particle is moving?
If the momentum of the particle is measured, what value is found(in terms of a & b)?
If the energy is measured, what value is found?
My Work:
\psi(x, t) = A exp[i(ax - bt)]
I took the partial derivatives wrt to t and x:
\frac{\partial \psi}{\partial t} = -(ib)\psi
\frac{\partial^2 \psi}{\partial x^2} = -a^2\psi
Time dependent Schrodinger's equation is:
i\hbar \frac{\partial \psi}{\partial t} = -\frac{\hbar^2}{2m}\frac{\partial^2 \psi}{\partial x^2} + V(x)\psi
Substituting the above values in this equation:
\hbar b \psi = \frac{\hbar^2 a^2}{2m}\psi + V(x)\psi
Dividing throughout by \psi and rearranging, I get the potential field as:
V(x) = \hbar\left(b - \frac{\hbar a^2}{2m}\right)
Am I going right? Before I can proceed furthur...
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