The stationary-state Schroedinger equation for U>E is a mathematical equation that describes the behavior of a quantum mechanical system with a potential energy greater than the total energy of the system. It is a time-independent equation and is used to find the probability distribution of the system in its stationary state.
The stationary-state Schroedinger equation is derived from the time-dependent Schroedinger equation by assuming that the system has reached a steady state and that the wave function does not change with time. This allows us to simplify the equation and solve for the stationary-state wave function and energy eigenvalues.
When the potential energy is greater than the total energy, it means that the system is in a bound state. This means that the system is confined to a specific region and cannot escape. The stationary-state Schroedinger equation allows us to calculate the probability of finding the system in different regions within the potential energy barrier.
The stationary-state Schroedinger equation is used in many practical applications, such as in the study of atomic and molecular structures, electrical conductivity in materials, and the behavior of quantum particles in potential wells. It is also essential in understanding and predicting the behavior of systems in quantum mechanics.
Yes, the stationary-state Schroedinger equation has its limitations. It only applies to systems in their stationary state and cannot be used to describe systems in non-stationary states. It also does not take into account relativistic effects and is limited to non-relativistic systems. Additionally, it assumes that the potential energy is time-independent, which may not always be the case in practical applications.