(If the equation below do not appear correctly, you can read all of the question in the attached file.)(adsbygoogle = window.adsbygoogle || []).push({});

Solving the time dependent 1D Schrödinger equation, one can show that in all points (x,t),

[tex] i\bar{h}\frac{\partial}{\partial t}\Psi(x,t)=-\frac{\bar{h}^2}{2m}\frac{\partial^2}{\partial x^2}\Psi(x,t)+V(x)\Psi(x,t)=E\Psi(x,t)[/tex]

for a certain value of the energy E. This means that the wave function is necessarily an eigenfunction of the hamiltonian operator.

On the other hand, we may specify an initial condition for this problem. My question is: what if the initial condition DOES NOT verify the above equations. Namely, if [tex]-\frac{\bar{h}^2}{2m}\frac{\partial^2}{\partial x^2}\Psi(x,t)+V(x)\Psi(x,t)[/tex] is not proportional to [tex]\Psi(x,t)[/tex].

Does it mean that not all initial conditions will give a solution or am I wrong somewhere? Thank you for your help!

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Initial condition for Schrödinger equation

Loading...

Similar Threads - Initial condition Schrödinger | Date |
---|---|

I How do I find this state |j,m=j> to calculate another state? | Aug 5, 2016 |

Initial conditions in quantum mechanics | Sep 13, 2013 |

Classical Stat Mech with Uncertain Initial Conditions vs. Quantum | Jan 2, 2012 |

**Physics Forums - The Fusion of Science and Community**