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It is given by the square of a mathematical function known as the "wavefunction", which is a solution of the Schrödinger equation. The lowest energy equilibrium state of the hydrogen atom is known as the ground state. The ground state wave function is known as the wavefunction.
This table shows the real hydrogen-like wave functions for all atomic orbitals up to 7s, and therefore covers the occupied orbitals in the ground state of all elements in the periodic table up to radium and some beyond. "ψ" graphs are shown with − and + wave function phases shown in two different colors (arbitrarily red and blue).
The wave function of the ground state of a hydrogen atom is a spherically symmetric distribution centred on the nucleus, which is largest at the center and reduces exponentially at larger distances. The electron is most likely to be found at a distance from the nucleus equal to the Bohr radius .
The ground state energy would then be 8E 1 = −109 eV, where E 1 is the Rydberg constant, and its ground state wavefunction would be the product of two wavefunctions for the ground state of hydrogen-like atoms: [2]: 262 (,) = (+) /. where a 0 is the Bohr radius and Z = 2, helium's nuclear charge.
The case = is called the ground state, its energy is called the zero-point energy, and the wave function is a Gaussian. [ 22 ] The harmonic oscillator, like the particle in a box, illustrates the generic feature of the Schrödinger equation that the energies of bound eigenstates are discretized.
Specifically, since the raising operator in the Segal–Bargmann representation is simply multiplication by = + and the ground state is the constant function 1, the normalized harmonic oscillator states in this representation are simply /!. At this point, we can appeal to the formula for the Husimi Q function in terms of the Segal–Bargmann ...
All calculations for such a system are performed on a two-dimensional subspace of the state space. If the ground state of a physical system is two-fold degenerate, any coupling between the two corresponding states lowers the energy of the ground state of the system, and makes it more stable.
The wave function of an initially very localized free particle. In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters ψ and Ψ (lower-case and capital psi, respectively). Wave functions are complex ...