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For instance, there is a big debate whether the decay process is reversible in time.
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The time reversibility is not a simple problem. The differential equation encases it wave function of the system, also called the quantum state or vector state 1 and 2. Schrodinger could work on the wave function by making use of the postulates of quantum mechanics. The name of this equation is after Erwin Schrodinger. The reason it seems like sometimes it's only the $t$ part that gets conjugated is simply that often it is the only part of the wavefunction that is complex. Furthermore, experts define the Schrodinger equation as the linear partial differential equation that can describe the wave function. $\Psi^*$ is the conjugate of that number, no more, no less. Several physicists, including de Broglie, Schrödinger and Bohm, believed that there should be, but although their efforts to find one still continue. It ensures that is a finite number so we can use it to calculate probabilities.For every $x$ and $t$, $\Psi(x,t)$ is a complex number. But while the wave function generally doesnt represent a straightforward wave in three-dimensional space, the question remains whether there is some sort of physical wave associated to it. This third condition follows from Born’s interpretation of quantum mechanics. The third condition requires the wave function be normalizable. (In a more advanced course on quantum mechanics, for example, potential spikes of infinite depth and height are used to model solids). Aim:- To solve the s-wave radial schrodinger equation for the vibrations of Hydrogen molecule. The second condition requires the wave function to be smooth at all points, except in special cases. The first condition avoids sudden jumps or gaps in the wave function.
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