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What value of a is required to normalize the function ?
To normalize a function, the value of a must be such that the integral of the function squared over its domain is equal to 1.
What is the integral of power in calculus?
The integral of a power function in calculus is found by adding 1 to the exponent and dividing by the new exponent. For example, the integral of xn is (x(n1))/(n1) C, where C is the constant of integration.
What is orthogonal and normalised wave function?
An orthogonal wave function is one that is perpendicular to another wave function within a given system. This means their inner product is zero. A normalised wave function is one that is scaled so that the integral of its square magnitude over all space is equal to 1. This normalization condition ensures that the probability of finding a particle in the system is always equal to 1.
How can one effectively normalize the wave function eix in quantum mechanics?
To effectively normalize the wave function eix in quantum mechanics, one must ensure that the integral of the absolute value of the wave function squared over all space is equal to 1. This involves finding the appropriate normalization constant to multiply the wave function by in order to satisfy this condition.
What is the Fourier transform of the function f(x) 1/r?
The Fourier transform of the function f(x) 1/r is 1/k, where k is the wave number.
What you the integral of 1?
if you are integrating with respect to x, the indefinite integral of 1 is just x
What is the integral of a function of x raised to the power of n multiplied by the derivative with respect to x of that same function of x with respect to x?
∫ f(x)nf'(x) dx = f(x)n + 1/(n + 1) + C n ≠-1 C is the constant of integration.
What is the integral of f divided by the quantity 1 minus f with respect to x where f is a function of x?
∫ f(x)/(1 - f(x)) dx = -x + ∫ 1/(1 - f(x)) dx
Why you use even and odd function in mathematics?
If you know that a function is even (or odd), it may simplify the analysis of the function, for several purposes. One example is the calculation of definite integrals: for an odd function, the integral of a function from (-x) to (x) (note 1) is zero; for an even function, this integral is twice the integral of the function from (0) to (x). Note 1: That is, the area under the function; for negative values, this "area" is taken as negative) is
What is a gamma function?
The gamma function is an extension of the concept of a factorial. For positive integers n, Gamma(n) = (n - 1)!The function is defined for all complex numbers z for which the real part of z is positive, and it is the integral, from 0 to infinity of [x^(z-1) * e^(-x) with respect to x.
What value of a is required to normalize the function ?
To normalize a function, the value of a must be such that the integral of the function squared over its domain is equal to 1.
What is the integral of the derivative with respect to x of the function f multiplied by the quantity a times f plus b raised to the power of n with respect to x?
∫ f'(x)(af(x) + b)n dx = (af(x) + b)n + 1/[a(n + 1)] + C C is the constant of integration.
What is the integral of 1 divided by the quantity of a function of x multiplied by the quantity of that same function plus or minus another function of x with respect to x?
∫ [1/[f(x)(f(x) ± g(x))]] dx = ±∫1/[f(x)g(x)] dx ± (-1)∫ [1/[g(x)(f(x) ± g(x))]] dx
What is the answer of 1 divide by x square?
What do you mean? As this is a calculus question, I presume that you are asking for a derivative or integral The derivative of any function of the form ƒ(x) = a * x ^ n is ƒ'(x) = a * n * x ^ (n-1) The integral of any function of the form ∫ a*x ^ n is a / (n+1) * x ^ (n+1) + C Your function that you gave is 1 / x^(2) which is equal to: x^(-2) Thus the derivative is: -2 * x^(-3) And the integral is: -x^(-1) + C
What is the integral of 1 divided by x with respect to x?
∫ (1/x) dx = ln(x) + C C is the constant of integration.
What is the integral of power in calculus?
The integral of a power function in calculus is found by adding 1 to the exponent and dividing by the new exponent. For example, the integral of xn is (x(n1))/(n1) C, where C is the constant of integration.
What is the integral of the derivative with respect to x of f divided by the quantity p squared plus q squared f squared with respect to x where f is a function of x and p and q are constants?
∫ f'(x)/(p2 + q2f(x)2) dx = [1/(pq)]arctan(qf(x)/p)
