Question

If there exist only one eigen function corresponding to a given eigen value, then the eigen value is called ____________

Answer 1

Answer:

Such an equation, where the operator, operating on a function, produces a constant times the function, is called an eigenvalue equation. The function is called an eigenfunction, and the resulting numerical value is called the eigenvalue. Eigen here is the German word meaning self or own......

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Answer 2

If there exists only one eigenfunction corresponding to a given eigenvalue, then the eigenvalue is called degenerate.

• An eigenvalue equation is one in which the operator, when applied to a function, yields a constant time the function. The function is referred to as an eigenfunction, and the resulting numerical value is referred to as an eigenvalue.
• Eigenfunctions are the function values that correspond to them. The Eigenfunctions of the Schrodinger equation, like those of a stretched string, must meet the following conditions:

1. The function must be single-valued and finite, which means that there is only one definite value of the function for each value of the variables x, y, and z.
2. Must be continuous, i.e., there must be no abrupt pursuit when its variables change.
3. At infinity, it must become zero.