tfhub said:Homework Statement
-h^2/2m (sqrt(2b/pi)) e^(-bx^2) d^2/dx^2 (e^(-bx^2)) dx from - to + infinity
Homework Equations
I tried differentiating e^(-bx^2) twice and it came up weird , I positioned the values and finally cam up with (-2b sqrt(pi/2b)...is there any other way to do it ?
The Attempt at a Solution
I tried with gaussian integration and my final answer is h^2b/m but it should be h^2b/2m... how am i missing the 1/2 factor?
There could be several reasons for this. One possibility is that there may be errors in the input data or in the method used for integration. Another possibility is that the underlying distribution may not actually be Gaussian, even though it appears to be. Additionally, numerical approximations and rounding errors can also contribute to discrepancies between the expected and actual results.
The accuracy of an integration result can be evaluated by comparing it with a known or expected value, or by running the integration with different methods and comparing the results. It is also important to check for potential sources of error, such as incorrect input data or numerical approximations, which can affect the accuracy of the result.
Yes, the shape of the distribution can have a significant impact on the integration result. Different integration methods may be more suitable for different types of distributions, and deviations from a Gaussian shape can also affect the accuracy of the result. It is important to choose an appropriate integration method for the specific distribution being analyzed.
Yes, there are several ways to improve the accuracy of an integration result. One approach is to use a more precise integration method, such as adaptive quadrature or Monte Carlo integration. It is also important to ensure that the input data is accurate and free of errors. Additionally, increasing the number of data points used in the integration can also improve the accuracy of the result.
If the integration result does not match the expected distribution, the first step is to check for potential sources of error, such as incorrect input data or an inappropriate integration method. It may also be helpful to visualize the data and compare it with the expected distribution, to see if there are any discrepancies. If the issue persists, it may be necessary to consult with experts or conduct further analysis to identify the cause of the mismatch.