Interesting Quantum Mechanics Problem

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SUMMARY

The discussion centers on the behavior of a particle in a one-dimensional infinite potential well, specifically addressing the first excited state where a node exists at x=a/2. Participants clarify that the particle does not 'travel' between the two halves of the box, as quantum mechanics does not define a well-defined path for particles. Instead, the particle's probability distribution allows for equal likelihood of being found in either half of the box, despite the presence of a node. This highlights the non-intuitive nature of quantum mechanics, where particles are treated as mathematical objects rather than classical entities.

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  • Basic concepts of probability distributions in quantum systems
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Students of quantum mechanics, physicists, and anyone interested in the foundational concepts of wave-particle duality and the behavior of particles in potential wells.

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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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