SpectraCat said:The Dirac delta function yield zero unless it's argument is zero, in which case it yields 1 (this is an oversimplification, but it should do for the present discussion). In your case, the argument of the delta function is [tex]-2*\pi + \epsilon[/tex], so it should be zero. Did you mean to type, [tex]\phi=\pi + \epsilon[/tex]? In that case, the argument of the delta function would be just [tex]\epsilon[/tex], and then you need to get a bit more specific about how you are defining the delta function. Have you looked at this thread? https://www.physicsforums.com/showthread.php?t=73447
haushofer said:With that specific range the delta distribution is zero; phi can't become equal to pi. So you get the equation 0 + k = T*0.
Delta Dirac, or Dirac delta function, is a mathematical function used in fields such as physics and engineering to model the behavior of point-like particles or impulses. It is defined as zero everywhere except at the origin, where it is infinite, with total area under the curve equal to one.
Delta Dirac is used in various scientific disciplines for its ability to model point-like behaviors and impulses. In physics, it is used to describe the behavior of particles at a specific point in space and time. In engineering, it is used to model impulses or forces acting on a system. It is also used in signal processing, probability theory, and quantum mechanics.
This equation is a specific form of the Dirac delta function, where $\epsilon$ represents a small positive number. It is used to model a narrow, high-amplitude spike at the point $\phi = -\pi$. The value of $\epsilon$ determines the width of the spike, with smaller values resulting in narrower spikes.
Delta Dirac is a generalized function, meaning it cannot be defined using a single mathematical equation. It is often represented as a limit of a sequence of functions, such as a Gaussian function, as the width of the spike approaches zero. It is also closely related to the Kronecker delta function, which is discrete rather than continuous.
Delta Dirac has various real-world applications, such as in signal processing to model impulses or sudden changes in a system. It is also used in quantum mechanics to describe the behavior of particles at a specific point in space and time. In electrical engineering, it is used to model electrical pulses. It is also used in probability theory to model point events.