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Particle in Infinite Potential Well (Rigid Box)
Particle in Infinite Potential Well (Rigid Box)
Published: 2014/03/02
Channel: AK LECTURES
Infinite square well (particle in a box)
Infinite square well (particle in a box)
Published: 2013/05/15
Channel: Brant Carlson
Wave Function of Particle in Finite Potential Well
Wave Function of Particle in Finite Potential Well
Published: 2014/03/05
Channel: AK LECTURES
One dimensional potential well energy eigen values and normalized eigen functions
One dimensional potential well energy eigen values and normalized eigen functions
Published: 2014/12/30
Channel: Physics Reporter
Lesson 19-20, Finite Square Well (updated)
Lesson 19-20, Finite Square Well (updated)
Published: 2012/10/06
Channel: Steve Spicklemire
Lecture - 40  Potential Well
Lecture - 40 Potential Well
Published: 2009/01/22
Channel: nptelhrd
What is gravitational potential (well)?
What is gravitational potential (well)?
Published: 2016/07/12
Channel: xmphysics
Particle in Finite Potential Well
Particle in Finite Potential Well
Published: 2014/03/05
Channel: AK LECTURES
11. Dispersion of the Gaussian and the Finite Well
11. Dispersion of the Gaussian and the Finite Well
Published: 2014/06/18
Channel: MIT OpenCourseWare
Quantum Mechanics (3) 2D Infinite Potential Well - Part 1
Quantum Mechanics (3) 2D Infinite Potential Well - Part 1
Published: 2014/09/21
Channel: Josh Pilipovsky
Visualizing Simple Harmonic Oscillators and the Double Well Potential
Visualizing Simple Harmonic Oscillators and the Double Well Potential
Published: 2014/12/12
Channel: Jake LaNasa
Quantum Well 9 : Finite Potential Well
Quantum Well 9 : Finite Potential Well
Published: 2011/10/03
Channel: Adam Beatty
PHYS3740 Lecture26-8 Finite Potential Well
PHYS3740 Lecture26-8 Finite Potential Well
Published: 2010/10/31
Channel: jmgerton
PHYS3740 Lecture24-1 Infinite Square Well
PHYS3740 Lecture24-1 Infinite Square Well
Published: 2010/10/26
Channel: jmgerton
ME564 Lecture 10: Examples of nonlinear systems: particle in a potential well
ME564 Lecture 10: Examples of nonlinear systems: particle in a potential well
Published: 2016/04/27
Channel: Steve Brunton
Mod-01 Lec-25 One-Dimensional Square Well Potential: The Bound State Problem
Mod-01 Lec-25 One-Dimensional Square Well Potential: The Bound State Problem
Published: 2013/03/04
Channel: nptelhrd
Quantum Particles in an Infinite Square Potential Well
Quantum Particles in an Infinite Square Potential Well
Published: 2009/07/12
Channel: wolframmathematica
Finite square well bound states
Finite square well bound states
Published: 2013/05/15
Channel: Brant Carlson
The Wavefunction - Solving the Infinite Square Well Potential
The Wavefunction - Solving the Infinite Square Well Potential
Published: 2015/10/27
Channel: Tristan Kleyn
quantum mechanics: infinite square well (part I)
quantum mechanics: infinite square well (part I)
Published: 2009/09/01
Channel: jrgoldma
Mod-01 Lec-26 The Square Well and the Square Potential Barrier
Mod-01 Lec-26 The Square Well and the Square Potential Barrier
Published: 2013/03/04
Channel: nptelhrd
Quantum Well 5 : Infinite Potential Well  -a/2 to a/2
Quantum Well 5 : Infinite Potential Well -a/2 to a/2
Published: 2011/09/26
Channel: Adam Beatty
Potential Energy vs. Internuclear Distance (Animated) : Dr. Amal K Kumar
Potential Energy vs. Internuclear Distance (Animated) : Dr. Amal K Kumar
Published: 2013/11/09
Channel: Dr.Amal K Kumar
Quantum Well 1 : Infinite Potential Well (Centered at Origin)
Quantum Well 1 : Infinite Potential Well (Centered at Origin)
Published: 2011/09/26
Channel: Adam Beatty
Particle in 1-dimensional infinite potential well (part 1)
Particle in 1-dimensional infinite potential well (part 1)
Published: 2015/06/03
Channel: MBPhysics
Particle in a Box - Infinite Potential Well
Particle in a Box - Infinite Potential Well
Published: 2011/03/24
Channel: David Foster
Finite Potential Well Example
Finite Potential Well Example
Published: 2014/03/06
Channel: AK LECTURES
Particle Moving Above Finite Potential Well
Particle Moving Above Finite Potential Well
Published: 2014/03/06
Channel: AK LECTURES
Lecture - 41  Potential Well
Lecture - 41 Potential Well
Published: 2009/01/22
Channel: nptelhrd
PHYS3740 Lecture26-1 Finite Potential Well
PHYS3740 Lecture26-1 Finite Potential Well
Published: 2010/10/31
Channel: jmgerton
12. The Dirac Well and Scattering off the Finite Step
12. The Dirac Well and Scattering off the Finite Step
Published: 2014/06/18
Channel: MIT OpenCourseWare
PARTICLE SCATTERING AND POTENTIAL WELL
PARTICLE SCATTERING AND POTENTIAL WELL
Published: 2016/06/11
Channel: Syafira Ramlan
Quantum Well 2 : Infinite potential well 0 to a
Quantum Well 2 : Infinite potential well 0 to a
Published: 2011/09/26
Channel: Adam Beatty
MP25 PARTICLE SCATTERING OF A POTENTIAL WELL
MP25 PARTICLE SCATTERING OF A POTENTIAL WELL
Published: 2014/06/11
Channel: Shazmeen Shamsuddin
Quantum Mechanics - Infinite square potential well.
Quantum Mechanics - Infinite square potential well.
Published: 2013/12/28
Channel: QuantumOverlord
Finite Square Well Bound States Part 1
Finite Square Well Bound States Part 1
Published: 2017/02/25
Channel: Dr. Underwood's Physics YouTube Page
Lecture 12 - Solving Schrodinger Equation, Stationary States, Infinite potential well
Lecture 12 - Solving Schrodinger Equation, Stationary States, Infinite potential well
Published: 2016/05/16
Channel: Tarek Ibrahim
Particle In an Infinite Potential Well (The Energy)
Particle In an Infinite Potential Well (The Energy)
Published: 2015/05/11
Channel: Everinus
Quantum Well 6: Infinite Potential Well -3a to 3a
Quantum Well 6: Infinite Potential Well -3a to 3a
Published: 2011/09/26
Channel: Adam Beatty
The bound state solution to the delta function potential TISE
The bound state solution to the delta function potential TISE
Published: 2013/05/15
Channel: Brant Carlson
L18.2 Phase shift for a potential well.
L18.2 Phase shift for a potential well.
Published: 2017/07/05
Channel: MIT OpenCourseWare
Finite square well scattering states
Finite square well scattering states
Published: 2013/05/15
Channel: Brant Carlson
Symmetric square well potentials
Symmetric square well potentials
Published: 2016/06/18
Channel: Andrew Nicoll
Quantum Well 3 : Infinite Potential Well 0 to 2a
Quantum Well 3 : Infinite Potential Well 0 to 2a
Published: 2011/09/26
Channel: Adam Beatty
Purdue PHYS 342 L2.6: Schrödinger Equation in 1D: The Finite Square Well
Purdue PHYS 342 L2.6: Schrödinger Equation in 1D: The Finite Square Well
Published: 2014/09/02
Channel: nanohubtechtalks
25. Normalizing The Finite Square Well | Learn Quantum Physics
25. Normalizing The Finite Square Well | Learn Quantum Physics
Published: 2015/04/21
Channel: Salah Salah
Wave packet in a potential well
Wave packet in a potential well
Published: 2013/04/10
Channel: Wouter Hordijk
Finite Potential Well
Finite Potential Well
Published: 2010/03/25
Channel: wolframmathematica
Lecture - 42  Potential Well
Lecture - 42 Potential Well
Published: 2009/01/22
Channel: nptelhrd
21.finite.square.well
21.finite.square.well
Published: 2012/10/25
Channel: utexascnsquest
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WIKIPEDIA ARTICLE

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A generic potential energy well.

A potential well is the region surrounding a local minimum of potential energy. Energy captured in a potential well is unable to convert to another type of energy (kinetic energy in the case of a gravitational potential well) because it is captured in the local minimum of a potential well. Therefore, a body may not proceed to the global minimum of potential energy, as it would naturally tend to due to entropy.

Overview[edit]

Energy may be released from a potential well if sufficient energy is added to the system such that the local maximum is surmounted. In quantum physics, potential energy may escape a potential well without added energy due to the probabilistic characteristics of quantum particles; in these cases a particle may be imagined to tunnel through the walls of a potential well.

The graph of a 2D potential energy function is a potential energy surface that can be imagined as the Earth's surface in a landscape of hills and valleys. Then a potential well would be a valley surrounded on all sides with higher terrain, which thus could be filled with water (e.g., be a lake) without any water flowing away toward another, lower minimum (e.g. sea level).

In the case of gravity, the region around a mass is a gravitational potential well, unless the density of the mass is so low that tidal forces from other masses are greater than the gravity of the body itself.

A potential hill is the opposite of a potential well, and is the region surrounding a local maximum.

Quantum confinement[edit]

Quantum confinement is responsible for the increase of energy difference between energy states and band gap, a phenomenon tightly related to the optical and electronic properties of the materials.

Quantum confinement can be observed once the diameter of a material is of the same magnitude as the de Broglie wavelength of the electron wave function.[1] When materials are this small, their electronic and optical properties deviate substantially from those of bulk materials.[2]

A particle behaves as if it were free when the confining dimension is large compared to the wavelength of the particle. During this state, the bandgap remains at its original energy due to a continuous energy state. However, as the confining dimension decreases and reaches a certain limit, typically in nanoscale, the energy spectrum becomes discrete. As a result, the bandgap becomes size-dependent. This ultimately results in a blueshift in light emission as the size of the particles decreases.

Specifically, the effect describes the phenomenon resulting from electrons and electron holes being squeezed into a dimension that approaches a critical quantum measurement, called the exciton Bohr radius. In current application, a quantum dot such as a small sphere confines in three dimensions, a quantum wire confines in two dimensions, and a quantum well confines only in one dimension. These are also known as zero-, one- and two-dimensional potential wells, respectively. In these cases they refer to the number of dimensions in which a confined particle can act as a free carrier. See external links, below, for application examples in biotechnology and solar cell technology.

Quantum mechanics view[edit]

Τhe electronic and optical properties of materials are affected by size and shape. Well-established technical achievements including quantum dots were derived from size manipulation and investigation for their theoretical corroboration on quantum confinement effect.[3] The major part of the theory is the behaviour of the exciton resembles that of an atom as its surrounding space shortens. A rather good approximation of an exciton’s behaviour is the 3-D model of a particle in a box.[4] The solution of this problem provides a sole[clarification needed] mathematical connection between energy states and the dimension of space. Decreasing the volume or the dimensions of the available space, increases the energy of the states. Shown in the diagram is the change in electron energy level and bandgap between nanomaterial and its bulk state.

The following equation shows the relationship between energy level and dimension spacing:

Research results[5] provide an alternative explanation of the shift of properties at nanoscale. In the bulk phase, the surfaces appear to control some of the macroscopically observed properties. However, in nanoparticles, surface molecules do not obey the expected configuration[which?] in space. As a result, surface tension changes tremendously.

Classical mechanics view[edit]

The classical mechanic explanation employs the Young-Laplace law to provide evidence on how pressure drop advances from scale to scale.

The Young-Laplace equation can give a background on the investigation of the scale of forces applied to the surface molecules:

Under the assumption of spherical shape R1=R2=R and resolving the Young-Laplace equation for the new radii R(nm), we estimate the new ΔP(GPa). The smaller the R, the greater the pressure is present. The increase in pressure at the nanoscale results in strong forces toward the interior of the particle. Consequently, the molecular structure of the particle appears to be different from the bulk mode, especially at the surface. These abnormalities at the surface are responsible for changes of inter-atomic interactions and bandgap.[6][7]

See also[edit]

References[edit]

  1. ^ M. Cahay (2001). Quantum Confinement VI: Nanostructured Materials and Devices : Proceedings of the International Symposium. The Electrochemical Society. ISBN 978-1-56677-352-2. Retrieved 19 June 2012. 
  2. ^ Hartmut Haug; Stephan W. Koch (1994). Quantum Theory of the Optical and Electronic Properties of Semiconductors. World Scientific. ISBN 978-981-02-2002-0. Retrieved 19 June 2012. 
  3. ^ Norris, DJ; Bawendi, MG (1996). "Measurement and assignment of the size-dependent optical spectrum in CdSe quantum dots". Physical Review B. 53 (24): 16338–16346. Bibcode:1996PhRvB..5316338N. PMID 9983472. doi:10.1103/PhysRevB.53.16338. 
  4. ^ Brus, L. E. (1983). "A simple model for the ionization potential, electron affinity, and aqueous redox potentials of small semiconductor crystallites". The Journal of Chemical Physics. 79 (11): 5566. Bibcode:1983JChPh..79.5566B. doi:10.1063/1.445676. 
  5. ^ Kunz, A B; Weidman, R S; Collins, T C (1981). "Pressure-induced modifications of the energy band structure of crystalline CdS". Journal of Physics C: Solid State Physics. 14 (20): L581. Bibcode:1981JPhC...14L.581K. doi:10.1088/0022-3719/14/20/004. 
  6. ^ H. Kurisu; T. Tanaka; T. Karasawa; T. Komatsu (1993). "Pressure induced quantum confined excitons in layered metal triiodide crystals". Jpn. J. Appl. Phys. 32 (Supplement 32–1): 285–287. Bibcode:1993JJAPS..32..285K. doi:10.7567/jjaps.32s1.285. 
  7. ^ Lee, Chieh-Ju; Mizel, Ari; Banin, Uri; Cohen, Marvin L.; Alivisatos, A. Paul (2000). "Observation of pressure-induced direct-to-indirect band gap transition in InP nanocrystals". The Journal of Chemical Physics. 113 (5): 2016. Bibcode:2000JChPh.113.2016L. doi:10.1063/1.482008. 

External links[edit]

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