What is potential and its significance in Quantum Mechanics?

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Potential in quantum mechanics refers to potential energy, which influences a particle's behavior. When potential is described as infinite in the Schrödinger Equation, it implies that the particle cannot move, effectively being "trapped." Conversely, a potential of zero indicates that the particle is free to move, as it possesses no potential energy. Understanding these concepts is crucial for interpreting quantum systems and their dynamics. The significance of potential lies in its role in determining particle behavior and energy states.
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what is potential mean Generally
? and what it mean in Quantum mechanics ?
 
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"Potential" by itself doesn't actually mean anything- but it is often used as shorthand for "potential energy". Do you know what that is?
 


explain please
 


Again, potential means potential energy.
 


okay in the shroodinger Equation when we say that the potential is infinite
and potential is zero ? is that mean ? the potential energy of particle infinite " the particle is stop to move "

at V =0 "it's mean particle free to move don't have potential Energy ?
 

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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