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SeM
Hi, I am wondering if there exists some general initial conditions for solving the Schödinger eqn. for 1D free electrons ?
Thanks!
Thanks!
Hi, I am doing a time-independent analysis, and thought of using the zero-point energy for E, in the Schrödinger eqn, and then solve it with the two initial conditions:stevendaryl said:Typically, in solving Schrodinger's equation, you are either doing a time-dependent analysis, in which case the initial conditions are part of the problem statement, or you are doing a time-independent analysis, in which case, people are usually looking for energy eigenstates.
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SeM said:Hi, I am doing a time-independent analysis, and thought of using the zero-point energy for E, in the Schrödinger eqn, and then solve it with the two initial conditions:
1) assume that the wavefunction is 1 at position zero (x=0), as it would be normalized to.
2) its slope, Psi', is zero at the same point, x=0. Does this sound reasonable?
Thanks
I know, there is another procedure to find the eigenstates. This is just to find the analytical solution to the ground state.stevendaryl said:If you already know a complete set of energy eigenstates then you can find a solution having those properties. Those properties don't help you find the eigenstates, though.
The Schrödinger equation is a mathematical equation that describes how the quantum state of a physical system changes over time. It was developed by Austrian physicist Erwin Schrödinger in 1925 and is a fundamental equation in quantum mechanics.
The initial conditions for the Schrödinger equation refer to the quantum state of a system at a specific starting point in time. This includes the position and momentum of all particles in the system, as well as any external forces or potentials acting on the system.
No, there are no typical initial conditions for the Schrödinger equation as they can vary greatly depending on the specific system being studied. Each quantum system has its own unique set of initial conditions that must be taken into account when solving the Schrödinger equation.
The initial conditions play a crucial role in determining the evolution of a quantum system according to the Schrödinger equation. They determine the probability of finding a particle in a certain position or state at a given time, and can greatly impact the behavior and properties of the system.
Yes, the Schrödinger equation is a deterministic equation that can be used to predict the future behavior of a quantum system. However, the inherent uncertainty of quantum mechanics means that the precise outcomes of measurements cannot be predicted, only the probability of different outcomes.