What is the combination of quantum numbers for the first excited state of a particle in a 3-D box ?
The ground state has only one wavefunction and no other state has this specific energy; the ground state and the energy level are said to be non-degenerate. However, in the 3-D cubical box potential the energy of a state depends upon the sum of the squares of the quantum numbers.
The particle having a particular value of energy in the excited state may has several different stationary states or wavefunctions. If so, these states and energy eigenvalues are said to be degenerate.
For the first excited state, three combinations of the quantum numbers (nx,ny,nz) are (2,1,1),(1,2,1),(1,1,2).
How to Calculate Zero Point Energy of Particle in 3D Box?
Zero Point Energy of Particle in 3D Box calculator uses Zero Point Energy of Particle in 3D Box = (3*([hP]^2))/(8*Mass of Particle*(Length of 3D Square Box)^2) to calculate the Zero Point Energy of Particle in 3D Box, The Zero Point Energy of Particle in 3D Box formula is defined as the lowest possible energy that a quantum mechanical system may have. Zero Point Energy of Particle in 3D Box is denoted by Z.P.E symbol.
How to calculate Zero Point Energy of Particle in 3D Box using this online calculator? To use this online calculator for Zero Point Energy of Particle in 3D Box, enter Mass of Particle (m) & Length of 3D Square Box (l) and hit the calculate button. Here is how the Zero Point Energy of Particle in 3D Box calculation can be explained with given input values -> 7.1E+38 = (3*([hP]^2))/(8*9E-31*(1E-19)^2).