# why nuclear forces doesnt follow principle of superposition?

Aman Bansal
592 Points
10 years ago

Dear Ranjita,

In physics and systems theory, the superposition principle , also known as superposition property, states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually. So that if input A produces response X and input B produces response Y then input (A + B) produces response (X + Y).

Mathematically, for a linear system, F, defined by F(x) = y, where x is some sort of stimulus (input) and y is some sort of response (output), the superposition (i.e., sum) of stimuli yields a superposition of the respective responses:

$F(x_1+x_2+\cdots)=F(x_1)+F(x_2)+\cdots$.

The superposition principle holds because, by definition, a linear system must be additive. Superposition may sometimes imply linearity, depending on whether homogeneity is included or implied in the definition of superposition.

In the field of electrical engineering, where the x and y signals are allowed to be complex-valued (as is common in signal processing), alinear system must satisfy the superposition property, which requires the system to be additive and homogeneous. An additive system satisfies $F(x_1 + x_2)= F(x_1) + F(x_2)$. A homogeneous system satisfies $F(a x)= a F(x)$, where a is a scalar. Often the additivity and homogeneity conditions for superposition are combined into a single condition, defined as

$F(a_1 x_1 + a_2 x_2)= a_1 F(x_1) + a_2 F(x_2)$,

for scalars a1 and a2

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Thanks

Aman Bansal