This quantum mechanical system by a particle of mass m confined in a one-dimensional box of length L. For the particle to be confined within region II, the potential energy outside (regions I and III) is assumed to be infinite.
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bouman.chem.georgetown.edu/S02/lect13/lect13.htm
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For a particle inside the box a free particle wavefunction is appropriate, but since the probability of finding the particle outside the box is zero, the wavefunction must go to zero at the walls. This constrains the form of the solution to...
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hyperphysics.phy-astr.gsu.edu/hbase/quantum/pbox.html
hyperphysics.phy-astr.gsu.edu/hbase/quantum/pbox.html
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The idealized situation of a particle in a box with infinitely high walls is an application of the Schrodinger equation which yields some insights into particle confinement. The wavefunction must be zero at the walls and the solution for the wavefunction yields just sine waves.
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hyperphysics.phy-astr.gsu.edu/hbase/quantum/schr.html
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At the ends of the line are large potential energy barriers that keep the particle within the "box." In the quantum-mechanical treatment of the problem the Schrödinger wave equation is used to calculate the allowed energies of the particle.
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www.chm.davidson.edu/ronutt/che115/Box/Box.htm
www.chm.davidson.edu/ronutt/che115/Box/Box.htm
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Click here for instructions ... You're browser does not support Java applets, alas.
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www.chem.uci.edu/undergrad/applets/dwell/dwell.htm
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The Particle in a One-Dimensional Box: ... The particle in a one-dimensional box model is one of the simplest models for electron behavior. In this model, the role of quantization becomes important in determining the energy eigenvalues of the electron.
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user.mc.net/~buckeroo/PODB.html
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The Quantum Mechanical Particle in a Box ... The Particle in a Box and its Symmetry ... The Particle in a Box Wave Function and Energy...
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jcbmac.chem.brown.edu/baird/QuantumPDF/lect5.html
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For the particle in a box, it can be shown that the average position is always , regardless of the state of the particle. In other words, the average position at which a particle in a box may be detected is exactly in the center of the quantum well;
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www.wikipedia.com/wiki/Particle_in_a_box
www.wikipedia.com/wiki/Particle_in_a_box
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A simple case to illustrate quantum mechanics is to consider a particle in a one-dimensional box. (A better description might be a bead on a string, but particle-in-a-box is the accepted name.)
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www.files.chem.vt.edu/chem-ed/quantum/pib1.html
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