Your attempt at a solution is not relevant to the question. To show that the given wavefunction is an eigenfunction, you need to operate on it with the Hamiltonian and see whether you get back the same wavefunction times a constant, in this case one of the energies ##E_n##.medofx said:
An eigenfunction is a special type of function in mathematics that returns a scalar multiple of itself when acted upon by a linear operator. In the context of the Schrödinger equation, an eigenfunction represents a state of the system with a specific energy value.
The Schrödinger equation is a fundamental equation in quantum mechanics that describes the time evolution of a quantum state. It is used to calculate the probability of a particle being in a certain state at a certain time, and to predict the behavior of quantum systems.
Eigenfunctions in the Schrödinger equation represent the possible states of a quantum system, and the corresponding eigenvalues represent the energy of those states. They play a crucial role in understanding the behavior and properties of quantum systems.
In the Schrödinger equation, an eigenfunction is associated with a specific eigenvalue, which represents the energy of that state. The eigenvalues are found by solving the Schrödinger equation, and the corresponding eigenfunctions are the solutions to the equation.
No, eigenfunctions cannot be directly observed in experiments. They are mathematical representations of the states of a quantum system and cannot be measured. However, the probability of a particle being in a certain state, represented by an eigenfunction, can be measured in experiments.
