Not all boundary conditions allow for solutions, but usually the physics suggests what makes sense.

They are equivalent to Dirichlet boundary conditions when the potential is known a-priori. An initial condition is like a boundary condition, but then for the time-direction.

A boundary condition expresses the behaviour of a function on the boundary (border) of its area of definition. Boundary conditions are a concept in differential equations. For instance if an object is grounded, the potential is known to be zero, and you have a Dirichlet boundary condition. Also note - boundary conditions are usually used to evaluate constants of integration when you are performing an indefinite integral. This is a boundary condition for a physics problem involving distance, velocity, and acceleration vs. time for the automobile that I am driving. Antiperiodic boundary conditions: They serve as a tool to inhibit unwanted longrange correlations or to study interfaces. $\begingroup$ PEC conditions are not necessarily equivalent to Dirichlet boundary conditions. This modification of the periodic boundary conditions is frequently used in lattice field theories.

It’s easy to see that with this boundary condition, a pulse will be reflected without change of sign. These boundary conditions are used in solid state physics. The concept is that the differential equation applies only to a certain region of space, or of any mathematical domain; time, frequency, momentum. The free end boundary condition for a string is, then, that its slope goes to zero at the boundary. A string is the limit of this picture with more and more rods, closer and closer together.

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