QM Integral and Online Integral Tables

In summary, The conversation is about an integral from Quantum Mechanics that the person is struggling with. They have searched for online integral tables but have not been able to find anything useful. They are inquiring about any decent online integral tables that are accessible to anyone, as they have found some online databases but they require a subscription. The person clarifies that A is a constant and not dependent on x, which allows for the integral to be reduced using a substitution and solved using the theorem of Fubini and polar plane coordinates. Another person suggests squaring the integral, transforming to polar coordinates, and using u-substitution to solve an easier integral. However, it is noted that no antiderivative exists for the integral in terms of familiar functions,
  • #1
longbusy
19
0
Hello, I am hung up on an integral from Quantum Mechanics. I searched on Yahoo and Google for online integral tables, but failed to discover anything beyond very basic tables. The integral is as follows:

[tex] \int_{-\infty}^{\infty} \(A*e^{-(x-a)^2} dx [/tex]

Are there any decent online integral tables that are accessible to just anyone? I found some online databases but quickly found out that I had to subscribe.

Thank You,
Jeremy
 
Last edited:
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  • #2
Is A just a constant or a matrix?
 
  • #3
cronxeh said:
Is A just a constant or a matrix?

The appropriate question would have bee:is A "x" dependent or not?


Daniel.
 
  • #4
Oops, sorry, A is a constant. It is not dependent upon x. I could have just left that out.
 
  • #5
In that case,it can be reduced (by a simple substitution) to a Poisson integral which is doable appling the thoerem of Fubini and polar plane coordinates...

Daniel.
 
  • #6
What he means is, square the integral and transform to polar coordinates, then use u-substitution (inverse chain rule) to solve an easy integral, take the square root of the result.

As a side note, it is impossible to find an antiderivative for your integral. No antiderivative exits (in terms of familiar functions).

As a side-side note, if a = 0 and A = 1, the answer is sqrt(pi)
 

FAQ: QM Integral and Online Integral Tables

What is a QM Integral?

A QM Integral, short for Quantum Mechanical Integral, is a mathematical expression used in quantum mechanics to calculate the probability of a particle being in a specific state or location. It is an essential tool for solving problems in quantum mechanics and is often represented as a complicated multi-dimensional integral.

How are QM Integrals calculated?

QM Integrals are typically solved using numerical methods, such as Monte Carlo or Gaussian Quadrature, due to their complexity. These methods involve breaking down the integral into smaller, more manageable parts and then using numerical approximations to solve them. Online Integral Tables provide pre-calculated values for commonly used QM Integrals, making it easier for scientists to use them in their calculations.

What are Online Integral Tables?

Online Integral Tables are digital databases that contain pre-calculated values for various mathematical integrals, including QM Integrals. These tables are useful for scientists and mathematicians as they provide quick access to values for commonly used integrals, saving time and effort in calculations.

How can Online Integral Tables be used in scientific research?

Online Integral Tables can be used in a variety of ways in scientific research. They can be used to verify the accuracy of calculations, to quickly find values for commonly used integrals, and to aid in the development of new mathematical models and theories. They are also useful for teaching and learning purposes.

Are there any limitations to using Online Integral Tables?

While Online Integral Tables are a valuable resource, they do have some limitations. These tables may not contain values for all possible integrals, and the accuracy of the pre-calculated values may vary. It is important for scientists to understand the limitations of these tables and use them appropriately in their research.

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