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This video discusses a problem with the variational method used to solve problems in mechanics. The problem is that the function is not continuous, and as a result, it is not a valid function to test in mechanics. The author shows how to solve this problem by first calculating the integral of the function "fiba" over the interval from 0 to 1. Next, they calculate the integral of the function "hamilton" over the interval from 0 to 2. Finally, they use the continuity equation to show that the function "w" is continuous over this interval.

**00:00:00**In this exercise, we are going to apply the variational method to the particle in a container using as a function of test the function x equal to n. We are going to calculate the percentage of error we make using this function as a function of test to describe the state fundamental of the particle in a container. The variational method is based on solving an integral called the variation of variations, which is usually represented by a w. This integral comes from the function of test expression which is the function of prueba. Hamilton's principle no longer holds as the function of test and is divided by the condition of normalization in the case that the function is not normalized. The integral will not give 1 and we have to divide it by the value of that integral according to the variational theorem. Variational variation is greater than or equal to the energy of the fundamental state in this case. Whenever we use a function of test, we always obtain a w that is greater than the real energy of the fundamental state and above the energy of the true state. We will draw the particle in a container and see what model wave function and energy is really because we know it is a model that has analytic solution and we know the function of wave as well as the energy we**00:05:00**In this video, a physicist explains how to calculate the integral of a function, using the variational principle. First, they calculate the integral of the function "fiba" over the interval from 0 to 1. Next, they calculate the integral of the function "hamilton" over the interval from 0 to 2. Finally, they use the continuity equation to show that the function "w" is continuous over this interval.**00:10:00**In this video, quantum mechanics is discussed, with particular focus on the method of variational calculus. In particular, problems 3.1 and 3.2 are discussed. It is shown that, when changing the x variable, the function will be either 0 or 1, depending on the value of a. When changing the x variable by a smaller amount, the function will be 0 again. This is continuous, and we can continue working with this safety in mind, knowing that the theorem of variation will be fulfilled and that the calculations I am making will be greater or equal to the true energy. We continue our function of test with our faith calculating now the integral of the numerator. Well We are going to continue calculating the integral of fib now. Well I'm going to subtract the constant from the derivative of x. x*x-x*cubed is the derivative of x with respect to x. x*x-x*cubed is equal to the derivative of x with respect to x-a, which is zero when x=0. This means that the function is continuous at x=0, and we can continue working with this safety in mind. The theorem of**00:15:00**The video discusses the quantum Mechanics method of variational calculus, which is used to solve problems involving the energy state of a quantum system. The video explains that, to calculate the error we have made in our calculations, we first need to know the true energy of the system's fundamental state. To do this, we change the value of w in our original equation by 1. This change in w results in a change in the corresponding quadrature term in our original equation, which we can then use to calculate the error we have made. The video shows how to do this by solving a problem involving a spring and a pendulum. The problem has an error of 1.32% and the video suggests that this error may be minimal if we are careful in our calculations.**00:20:00**In the video, the author discusses a problem with the variational method used to solve problems in mechanics. The problem is that the function is not continuous, and as a result, it is not a valid function to test in mechanics.

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