# Solution of radial equation for hydrogen atom

The key to solving the hydrogen atom is to take advantage of the spherical symmetry, i.e., convert to radial coordinates (r,θ,φ). The potential part of the Hamiltonian is already in radial form, so it’s just a matter of getting the kinetic energy operator into the radial coordinates. This is a standard exercise in Solutions of Schrodinger's equation for the Hydrogen atom can be factorize in a function of the distance of the electron from the nucleus (r) and a function of the direction (ϑ, ϕ), due to the spherical symmetry of the problem. Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Different approaches to the solution of the radial equation for the hydrogen atom are examined. We point out several important issues: In the conventional series solution method, when two roots of ... Radial equation solutions • Using a separation of the hydrogen atom wavefunction solutions into radial and angular parts • And rewriting the radial part using We obtained the radial equation • Where we know l is 0 or any positive integer • We now choose to write our energies in the form Where n for now is just an arbitrary real number

Frequently the hydrogen atom eigenvalue problem is analytically solved by solving a radial wave equation for a particle in a Coulomb field. In this article, complex coordinates are introduced, and an expression for the energy levels of the hydrogen atom is obtained by means of the algebraic solution of operators. Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. 5. Wang Z, Chen Q (2005) Exact Solution of the N-dimensional Radial Schrödinger Equation via Laplace Transformation Method with the Generalized Cornell Potential. Comp Phys Comm 179: 49. 6. Al-Jaber SM (1998) Hydrogen Atom in N Dimensions. Int J Theor Phys 37: 1289-1298. 7. 7.1 Application of the Schrödinger Equation to the Hydrogen Atom 7.2 Solution of the Schrödinger Equation for Hydrogen 7.3 Quantum Numbers 7.4 Magnetic Effects on Atomic Spectra – Normal Zeeman Effect 7.5 Intrinsic Spin 7.6 Energy Levels and Electron Probabilities CHAPTER 7 The Hydrogen Atom By recognizing that the chemical atom is composed ...

7.1 Application of the Schrödinger Equation to the Hydrogen Atom 7.2 Solution of the Schrödinger Equation for Hydrogen 7.3 Quantum Numbers 7.4 Magnetic Effects on Atomic Spectra – Normal Zeeman Effect 7.5 Intrinsic Spin 7.6 Energy Levels and Electron Probabilities CHAPTER 7 The Hydrogen Atom By recognizing that the chemical atom is composed ... hydrogen atom is a two-particle system, and as a preliminary to dealing with the H atom, we first consider a simpler case, that of two noninteracting particles. Suppose that a system is composed of the noninteracting particles 1 and 2. I'm trying to solve Schrödinger 1D equation for hydrogen atom but I found several difficulties. To get in context I want to solve this equation . For Z and l real and arbitraries. To start with I tried for Z=1 and l=0 and I tried in the following way

The detailed analysis to find spherical solution of equation (9) is discussed in Shpenkov’s other papers [9, 11]. Some consequences of the solution of the Shpenkov’s interpretation of classical wave equation are [6]: a. As masses of atoms are multiple of the neutron mass (or hydrogen atom mass), following