page_title: Quantum mechanics
section_title: Step potential
hierarchical_section_title: Quantum mechanics / Examples / Step potential
caption_attribution_description: English: 1d step potential in quantum mechanics.
context_page_description: Quantum mechanics is a fundamental theory in physics that describes the physical properties of nature at small scales, of the order of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science.
  Classical physics, the description of physics that existed before the theory of relativity and quantum mechanics, describes many aspects of nature at an ordinary scale, while quantum mechanics explains the aspects of nature at small scales, for which classical mechanics is insufficient.
  Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large scale. Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values, objects have characteristics of both particles and waves, and there are limits to how accurately the value of a physical quantity can be predicted prior to its measurement, given a complete set of initial conditions.
context_section_description: The potential in this case is given by:
  The solutions are superpositions of left- and right-moving waves:
  and
  ,
  with coefficients A and B determined from the boundary conditions and by imposing a continuous derivative on the solution, and where the wave vectors are related to the energy via
  and
  .
  Each term of the solution can be interpreted as an incident, reflected, or transmitted component of the wave, allowing the calculation of transmission and reflection coefficients. Notably, in contrast to classical mechanics, incident particles with energies greater than the potential step are partially reflected.
caption: Scattering at a finite potential step of height V0, shown in green. The amplitudes and direction of left- and right-moving waves are indicated. Yellow is the incident wave, blue are reflected and transmitted waves, red does not occur. E > V0 for this figure.
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