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why is (psi)n=Asin(npix/L) the energy eigenvalue?
An energy eigenvalue is a value that represents the energy of a specific state or level of a quantum mechanical system. It is a fundamental concept in quantum mechanics and is used to describe the behavior and properties of particles at the atomic and subatomic level.
The energy eigenvalue is represented by the variable n in the equation. It is multiplied by the constant h (Planck's constant) and divided by the wavelength of the particle (λ) to calculate the energy of a particular state.
The wave function (psi) represents the probability amplitude of a particle being in a specific state. In quantum mechanics, particles are described as waves, and the sine function is a common wave function used to describe the behavior of particles in a confined space.
The constant A in the energy eigenvalue equation represents the amplitude of the wave function. It is a normalization constant that ensures the probability amplitude is always between 0 and 1.
The length of the box (L) is a crucial factor in determining the energy eigenvalues of a system. As the length of the box changes, the allowed energy levels of the system also change. This is because the standing waves inside the box must have an integer number of half-wavelengths to satisfy the boundary conditions, resulting in different energy eigenvalues.