Solving for A in 1 = A2∫-2(x/a)2sin2(kx)

• jocdrummer
In summary, the conversation is about a homework question in Quantum Mechanics involving a math problem with an integral. The goal is to solve for the constant A and the integral is from -inf to inf. The suggestion is to use the formula for sin(kx) and complete the squares, followed by a change of variables to convert to real integrals.
jocdrummer
This is actually part of a homework question for my Quantum Mechanics course but it is purely a math question.

1 = A2$$\int$$e-2(x/a)2sin2(kx)

Note: for some reason the integral is showing up as a psi.

where A, a, and k are constants and the integral is from -inf to inf (or 0 to inf with a constant 2 multiplying because the integrand is symmetric)

What I am trying to do is solve for A. For the integral, there aren't any common forms that it matches up with that I am aware of. I've tried IBP but it seems to just get more and more complicated as it goes along. Any suggestions would be awesome.

i'm gussing the limits are -inf to inf, this should help simplify things as
$$\int_{-\infty}^{\infty} dx.e^{-x^2} = \sqrt{\pi}$$

I think a few IBPs is the right way to though it will be pretty messy

Don't do parts. Use that sin(kx)=(exp(i*k*x)-exp(-i*k*x))/(2i). Expand everything and complete the squares. Then do a change of variables on each integral to convert everything to real integrals.

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What is the equation 1 = A2∫-2(x/a)2sin2(kx) used for?

The equation 1 = A2∫-2(x/a)2sin2(kx) is used to solve for the value of A in a given mathematical expression.

How do I solve for A in the equation 1 = A2∫-2(x/a)2sin2(kx)?

To solve for A, you can use algebraic manipulation and mathematical principles to isolate A on one side of the equation. This may involve using the distributive property, combining like terms, and applying the inverse of any operations being used.

What do the variables in the equation 1 = A2∫-2(x/a)2sin2(kx) represent?

The variable A represents the unknown value that we are trying to solve for. The variable x represents the independent variable, while k represents a constant. The integral and sine functions are mathematical operations.

Are there any restrictions on the values of the variables in 1 = A2∫-2(x/a)2sin2(kx)?

Yes, there may be restrictions on the values of the variables in order to ensure that the equation is valid and the solution is meaningful. For example, the value of A cannot be equal to zero, as this would result in a division by zero error. Additionally, the values of x and k may need to be within a certain range for the equation to make sense.

How can I check that my solution for A in 1 = A2∫-2(x/a)2sin2(kx) is correct?

You can check your solution by substituting the value of A into the original equation and seeing if it satisfies the equation. You can also use a graphing calculator or software to graph the equation and see if your solution aligns with the graph.

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