Normalization said:
tiny-tim said:I'm not convinced you've got this.
They have integrated that big bracket, and so they also differentiate the x (to get 1) …
the […] term is 0 (so they haven't written it), and that only leaves the ∫ term, which always has a minus in front of it.
Integration by parts is a method used in calculus to evaluate integrals that involve products of functions. It involves using the product rule from differentiation to transform the integral into a different form that is easier to solve.
To use integration by parts, you must first choose two functions, usually denoted as u and v, and apply the product rule to find their derivatives. Then, you can rewrite the original integral as a combination of these derivatives and solve it using the integration by parts formula.
The derivative of expectation value problem often involves integrals that can be difficult or impossible to solve using basic integration techniques. Integration by parts allows us to transform these integrals into a more manageable form, making it easier to find the solution.
The integration by parts formula is ∫u dv = uv - ∫v du, where u and v are the two functions chosen and du and dv are their corresponding derivatives.
While integration by parts is a powerful tool, it does have its limitations. It may not be applicable to all integrals, and it can sometimes lead to more complex integrals that are still difficult to solve. It is important to carefully choose the functions u and v to ensure that integration by parts is the most effective method for solving the integral.