Interesting Quantum Mechanics Problem

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In the discussion of a quantum mechanics problem involving a particle in a box with infinite potential outside defined boundaries, the focus is on the implications of the first excited state, which features a node at x=a/2. This node indicates a zero probability of finding the particle at that position, raising questions about how the particle can be considered to "travel" between the two halves of the box. The consensus is that in quantum mechanics, there is no traditional concept of travel; the particle exists as a probability distribution rather than a defined path. The particle can be observed with equal probability in either half of the box, and the node can be interpreted as part of the particle's wave function, representing a complex behavior that diverges from classical intuition. This highlights the non-intuitive nature of quantum mechanics, where particles are treated as mathematical entities rather than physical objects with straightforward properties.
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Interesting Quantum Mechanics Problem

Suppose we have a particle in a box with infinite potential for x>a and x<0 and zero potential in between.Then by solving the schrd. equation we get a node at x= a/2 for first excited state.Which means the probability of finding the particle at x=a/2 is zero for all times if it is a stationary first excited state.
Then how does the particle travel from one half of the box to the another without encountering the node.I know there is no well defined path but still space is well-connected and have no loops or whatever. I am feeling quite uneasy regarding this.

please...enlightment.
 
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There is no 'travel', just like you said. The particle always has an equal probability of being observed in either half of the box; you can't say it's ever in one or the other, nor that it is traveling between them.
I am feeling quite uneasy regarding this.
Welcome to the world of QM. :wink: The universe is just really weird; eventually you will get used to it.
 
Basicly, this node IS particle itself (along with two maxima). Or consider it to be sum of two "parts" of the particle traveling in opposite directions.

Particles (=waves) are mathematical objects, and their properties do not have to be the same as properties of baseball or ocean wave.
 
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