Dirac Delta Potential

Dirac-Delta pot" : (Attractive D.D Poty) Consider a particle of mass 'm' in the poth V(x) = ... Vo > 0 & Rea Const. Cases (i) ELO (ii) E>O The function is zero for all values of x except at x=0, where it is negative infinity. The text below introduces two cases for analysis: E<0 and E>0. The overall presentation is clear and concise. The equations involve variables such as x, V(x), E, m, and Ψ(x), which are commonly used in quantum mechanics to represent position, potential energy, total energy, mass, and wavefunction, respectively. The image presents handwritten equations and text related to quantum mechanics. It involves wavefunctions represented by Y, constants A, B, C, D, k, and n, as well as regions labeled I and II. The image contains handwritten text related to quantum mechanics, specifically discussing boundary conditions for a wavefunction in a particular region (Region II) defined by x > 0. The text mentions the rejection of a certain condition (Bec), the acceptance of another (B=0), and introduces a wavefunction solution (Ψ1 = Ae^(400/8)). The text mentions the behavior of constants C and D at infinity, the condition for the wavefunction to be finite, and a proposed solution for the wavefunction in Region II. The equations involve variables such as Ψ, A, B, C, D, and k, which are commonly used to represent wavefunctions, coefficients, and wave numbers. The text also includes conditions for the wavefunctions in each region. The overall presentation is clear, with equations organized in a logical manner. The equations involve variables such as Ψ, A, B, k, and η. The text mentions bound states and the behavior of the wavefunction at infinity. The handwriting is clear, but the context and meaning of the equations are difficult to determine without further information. The text mentions the behavior of the wavefunction at infinity, the continuity of the wavefunction and its derivative at boundaries, and the concept of discontinuity. The equations involve variables such as Ψ, x, and y, which are commonly used in quantum mechanics. The handwriting is clear in some parts but becomes illegible in others, making it difficult to interpret certain parts of the text. The overall layout is disorganized, with equations and text scattered across the page. The content appears to be related to quantum mechanics or wave mechanics, potentially involving the Schrödinger equation or related concepts. The handwriting is clear in some parts, but becomes illegible in others, making it difficult to interpret certain parts of the text. The overall layout is disorganized, with equations scattered across the page. [lim_{E\rightarrow0}[\frac{d~\psi}{d\pi t}|_{u=\pm\epsilon}-\frac{d~\psi}{dm}\int_{u=-6}^{-6}\overline{4}]+\frac{d~mE}{\xi}[im](\varphi(u_{in)d_{0}}] [+lim_{E\rightarrow0}\frac{2mV_{0}}{\hbar^{2}}\int_{-E}^{E}\frac{E}{}\frac{E}{i!}\int_{-E}^{\chi_{0}}du=0] [\int_{-x_{e}}^{x_{o}}f(\tau)\delta[\tau-0]d\tau\ =f(a)\end{aligned}] [{E^{-1/m}(\frac{dh_{y}}{d~u}\int_{u=+\epsilon}\frac{d~t}{d\pi}|_{x\in E})+\frac{d~m~v_{o}}{\hbar^{2}}\varphi(c)=0}] Einstein's equation relating energy (E) to mass (m) and the speed of light (c), and Newton's second law of motion relating force (F) to mass (m) and acceleration (a). The equations are written in a clear and concise manner. The equations include variables such as K, A, m, Vo, and E. There are also numerical values and symbols like square roots and equal signs. The handwriting is clear, but the specific meaning and context of the equations are difficult to determine without further information. The overall layout is organized, with equations presented in a vertical column. The equations involve variables such as Ψ, x, and y, which are commonly used in quantum mechanics. The handwriting is clear in some parts, but becomes illegible in others, making it difficult to interpret certain parts of the text. The overall layout is disorganized, with equations and text scattered across the page. Integral from -infinity to infinity of |psi(x)|^2 dx equals 1 Integral from -infinity to infinity of |Ae^(ikx)|^2 dx equals 1 Integral from -infinity to infinity of A^2e^(2ikx) dx equals 1 A^2 * [1/(2ik) * e^(2ikx)] from -infinity to infinity equals 1 (A^2)/(2ik) * [e^(infinity) - e^(-infinity)] equals 1 A^2 / 2 equals 1 |A|^2 equals K |A| equals sqrt(K) This is a famous equation in physics representing the equivalence of mass and energy. The equation is centered and written in clear, uppercase letters. Ψ(x) = Ae^(ikx) + Be^(-ikx) Ψ(x) = Ae^(ikx) + Ae^(-ikx) = 2Acosh(kx) The equations involve variables such as Ψ, x, and y, which are commonly used in quantum mechanics. The handwriting is clear in some parts, but becomes illegible in others, making it difficult to interpret certain parts of the text. The overall layout is disorganized, with equations and text scattered across the page. The equations involve variables such as x, ψ, η, φ, and constants like 0 and 1. The overall presentation is messy and difficult to read, with inconsistent spacing and handwriting. The specific meaning and context of the equations are unclear without further information. The image contains two famous equations from physics: Einstein's equation relating energy (E) to mass (m) and the speed of light (c), and Newton's second law of motion relating force (F) to mass (m) and acceleration (a). The equations are written in a clear and concise manner. The image contains two famous equations from physics: Einstein's equation relating energy (E) to mass (m) and the speed of light (c), and Newton's second law of motion relating force (F) to mass (m) and acceleration (a). The equations are written in a clear and concise manner. The content appears to be derivations or calculations involving wave functions or related concepts. The handwriting is generally clear, but some symbols are difficult to interpret. The equations are organized in a vertical column with some intermediate steps shown.