High like-probability amplitude ;)
I have been studying Physics for two decades now, but never have "seen" Quantum Mechanics at work- this app is awesome!!
Quantum Wave in a Box
Разработчик:
Michel Ramillon
Описание
Schrödinger equation solver 1D. User defined potential V(x). Diagonalization of hamiltonian matrix. Animation showing evolution in time of a gaussian wave-packet.
In Quantum Mechanics the one-dimensional Schrödinger equation is a fundamental academic though exciting subject of study for both students and teachers of Physics. A solution of this differential equation represents the motion of a non-relativistic particle in a potential energy field V(x). But very few solutions can be derived with a paper and pencil.
Have you ever dreamed of an App which would solve this equation (numerically) for each input of V(x) ?
Give you readily energy levels and wave-functions and let you see as an animation how evolves in time a gaussian wave-packet in this particular interaction field ?
Quantum Wave in a Box does it ! For a large range of values of the quantum system parameters.
Actually the originally continuous x-spatial differential problem is discretized over a finite interval (the Box) while time remains a continuous variable. The time-independent Schrödinger equation H ψ(x) = E ψ(x), represented by a set of linear equations, is solved by using quick diagonalization routines. The solution ψ(x,t) of the time-dependent Schrödinger equation is then computed as ψ(x,t) = exp(-iHt) ψ₀(x) where ψ₀(x) is a gaussian wave-packet at initial time t = 0.
You enter V(x) as RPN expression, set values of parameters and will get a solution in many cases within seconds !
- Atomic units used throughout (mass of electron = 1)
- Quantum system defined by mass, interval [a, b] representing the Box and (real) potential energy V(x).
- Spatially continuous problem discretized over [a, b] and time-independent Schrödinger equation represented by a system of N+1 linear equations using a 3, 5 or 7 point stencil; N being the number of x-steps. Maximum value of N depends on device’s RAM: up to 4000 when computing eigenvalues and eigenvectors, up to 8000 when computing eigenvalues only.
- Diagonalization of hamiltonian matrix H gives eigenvalues and eigenfunctions. When computing eigenvalues only, lowest energy levels of bound states (if any) with up to 10-digit precision.
- Listing of energy levels and visualisation of eigenwave-functions.
- Animation shows gaussian wave-packet ψ(x,t) evolving with real-time evaluation of average velocity, kinetic energy and total energy.
- Toggle between clockwise and counter-clockwise evolution of ψ(x,t).
- Watch Real ψ, Imag ψ or probability density |ψ|².
- Change initial gaussian parameters of the wave-packet (position, group velocity, standard deviation), enter any time value, then tap refresh button to observe changes in curves without new diagonalization. This is particularly useful to get a (usually more precise) solution for any time value t when animation is slower in cases of N being large.
- Watch both solution ψ(x,t) and free wave-packet curves evolve together in time and separate when entering non-zero potential energy region.
- Zoom in and out any part of the curves and watch how ψ(x,t) evolve locally.
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In Quantum Mechanics the one-dimensional Schrödinger equation is a fundamental academic though exciting subject of study for both students and teachers of Physics. A solution of this differential equation represents the motion of a non-relativistic particle in a potential energy field V(x). But very few solutions can be derived with a paper and pencil.
Have you ever dreamed of an App which would solve this equation (numerically) for each input of V(x) ?
Give you readily energy levels and wave-functions and let you see as an animation how evolves in time a gaussian wave-packet in this particular interaction field ?
Quantum Wave in a Box does it ! For a large range of values of the quantum system parameters.
Actually the originally continuous x-spatial differential problem is discretized over a finite interval (the Box) while time remains a continuous variable. The time-independent Schrödinger equation H ψ(x) = E ψ(x), represented by a set of linear equations, is solved by using quick diagonalization routines. The solution ψ(x,t) of the time-dependent Schrödinger equation is then computed as ψ(x,t) = exp(-iHt) ψ₀(x) where ψ₀(x) is a gaussian wave-packet at initial time t = 0.
You enter V(x) as RPN expression, set values of parameters and will get a solution in many cases within seconds !
- Atomic units used throughout (mass of electron = 1)
- Quantum system defined by mass, interval [a, b] representing the Box and (real) potential energy V(x).
- Spatially continuous problem discretized over [a, b] and time-independent Schrödinger equation represented by a system of N+1 linear equations using a 3, 5 or 7 point stencil; N being the number of x-steps. Maximum value of N depends on device’s RAM: up to 4000 when computing eigenvalues and eigenvectors, up to 8000 when computing eigenvalues only.
- Diagonalization of hamiltonian matrix H gives eigenvalues and eigenfunctions. When computing eigenvalues only, lowest energy levels of bound states (if any) with up to 10-digit precision.
- Listing of energy levels and visualisation of eigenwave-functions.
- Animation shows gaussian wave-packet ψ(x,t) evolving with real-time evaluation of average velocity, kinetic energy and total energy.
- Toggle between clockwise and counter-clockwise evolution of ψ(x,t).
- Watch Real ψ, Imag ψ or probability density |ψ|².
- Change initial gaussian parameters of the wave-packet (position, group velocity, standard deviation), enter any time value, then tap refresh button to observe changes in curves without new diagonalization. This is particularly useful to get a (usually more precise) solution for any time value t when animation is slower in cases of N being large.
- Watch both solution ψ(x,t) and free wave-packet curves evolve together in time and separate when entering non-zero potential energy region.
- Zoom in and out any part of the curves and watch how ψ(x,t) evolve locally.
Скриншоты
Quantum Wave in a Box Частые Вопросы
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Приложение Quantum Wave in a Box бесплатное?
Да, Quantum Wave in a Box полностью бесплатное и не содержит встроенных покупок или подписок.
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Является ли Quantum Wave in a Box фейковым или мошенническим?
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Сколько стоит Quantum Wave in a Box?
Приложение Quantum Wave in a Box бесплатное.
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Quantum Wave in a Box Конкуренты
| Name | Скачивания (30d) | Ежемесячный доход | Отзывы | Оценки | Последнее обновление | |
|---|---|---|---|---|---|---|
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1 год назад | |
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Feel quantum!
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0
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7 месяцев назад |
Quantum Wave in a Box Установки
30дн.
Quantum Wave in a Box Доход
30дн.Quantum Wave in a Box Доходы и Загрузки
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Информация о приложении
- Категория
- Education
- Разработчик
- Michel Ramillon
- Языки
- English
- Последнее обновление
- 1.0.3 (1 год назад )
- Выпущено
- Jan 1, 2017 (7 лет назад )
- Также доступно в
- Франция , Соединенные Штаты , Германия , Испания , Великобритания , Малайзия , Новая Зеландия , Норвегия , Нидерланды , Нигерия , Филиппины , Мексика , Латвия , Ливан , Казахстан , Кувейт , Республика Корея , Перу , Индия , Пакистан , Польша , Румыния , Россия , Саудовская Аравия , Швеция , Сингапур , Таиланд , Турция , Тайвань , Украина , Вьетнам , Южно-Африканская Республика , Дания , Аргентина , Австрия , Австралия , Азербайджан , Бельгия , Бразилия , Беларусь , Канада , Швейцария , Чили , Китай , Колумбия , Чехия , Япония , Доминиканская Республика , Алжир , Эквадор , Египет , Финляндия , Греция , Гонконг (САР) , Венгрия , Индонезия , Ирландия , Израиль , ОАЭ , Италия
- Обновлено
- 3 дня назад
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