The WF will be cosh in the middle, and exponential on either side.kt7888 said:so how would you normalize a dirac function with a potential V(x)=-αδ(x+a)-αδ(x-a)
well...write a normalizable solution to time ind. schrodinger eq. in the three regions?
PLEASE HELP ASAP!
The Dirac-delta function, also known as the Dirac delta distribution, is a mathematical function that is defined as zero everywhere except at the origin, where it is infinite. It is used in mathematical and scientific fields to represent a point mass or impulse in a system.
The Dirac-delta function is used to model and analyze systems that involve sudden, instantaneous changes or impulses. It is also used to represent point sources in fields such as electromagnetism and quantum mechanics.
The Dirac-delta function is defined as a limit of a sequence of functions that become increasingly narrow and tall, with the area under the curve equal to one. In other words, it is a mathematical construct that approximates a point mass or impulse at the origin.
Some key properties of the Dirac-delta function include: it is even, i.e. δ(-x) = δ(x); it is infinitely tall at the origin, i.e. δ(x) = ∞ at x = 0; it is zero everywhere else, i.e. δ(x) = 0 for x ≠ 0; and it integrates to one, i.e. ∫δ(x)dx = 1.
The Dirac-delta function is used in a variety of fields, including physics, engineering, and signal processing. It is commonly used to represent point sources such as particles or point charges, and to analyze systems that involve impulses or sudden changes. It is also used in the Fourier transform to represent periodic signals and in the Laplace transform to solve differential equations with initial conditions.