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What (who) is quartic equation - definition
Quartic equation
![minima]] were above the ''x'' axis, or if the local [[maximum]] were below it, or if there were no local maximum and one minimum below the ''x'' axis, there would only be two real roots (and two complex roots). If all three local extrema were above the ''x'' axis, or if there were no local maximum and one minimum above the ''x'' axis, there would be no real root (and four complex roots). The same reasoning applies in reverse to polynomial with a negative quartic coefficient.](https://commons.wikimedia.org/wiki/Special:FilePath/Polynomialdeg4.svg?width=200 "minima]] were above the ''x'' axis, or if the local [[maximum]] were below it, or if there were no local maximum and one minimum below the ''x'' axis, there would only be two real roots (and two complex roots). If all three local extrema were above the ''x'' axis, or if there were no local maximum and one minimum above the ''x'' axis, there would be no real root (and four complex roots). The same reasoning applies in reverse to polynomial with a negative quartic coefficient.")
FUNCTION DEFINED BY A POLYNOMIAL OF DEGREE FOUR
Biquadratic equation; Biquadratic; Quartic polynomial; Quartic equations; Quartic formula; Fourth degree polynomial; Quartic Equation; Ferrari's method; Forth order polynomial; Biquadratic function; Biquadratic polynomial; Fourth degree equation; Fourth-degree equation; Valmes; Paolo Valmes; Depressed quartic; Y=ax^4+bx^3+cx^2+dx+e; Y=ax4+bx3+cx2+dx+e; Fourth order polynomial
In mathematics, a quartic equation is one which can be expressed as a quartic function equaling zero. The general form of a quartic equation is
Biquadratic
FUNCTION DEFINED BY A POLYNOMIAL OF DEGREE FOUR
Biquadratic equation; Biquadratic; Quartic polynomial; Quartic equations; Quartic formula; Fourth degree polynomial; Quartic Equation; Ferrari's method; Forth order polynomial; Biquadratic function; Biquadratic polynomial; Fourth degree equation; Fourth-degree equation; Valmes; Paolo Valmes; Depressed quartic; Y=ax^4+bx^3+cx^2+dx+e; Y=ax4+bx3+cx2+dx+e; Fourth order polynomial
·noun A biquadratic equation.
II. Biquadratic ·noun A Biquadrate.
III. Biquadratic ·adj Of or pertaining to the biquadrate, or fourth power.
Schrödinger equation
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![[[Erwin Schrödinger]]](https://commons.wikimedia.org/wiki/Special:FilePath/Erwin Schrodinger2.jpg?width=200 "[[Erwin Schrödinger]]")
![spring]], oscillates back and forth. (C–H) are six solutions to the Schrödinger Equation for this situation. The horizontal axis is position, the vertical axis is the real part (blue) or imaginary part (red) of the [[wave function]]. [[Stationary state]]s, or energy eigenstates, which are solutions to the time-independent Schrödinger equation, are shown in C, D, E, F, but not G or H.](https://commons.wikimedia.org/wiki/Special:FilePath/QuantumHarmonicOscillatorAnimation.gif?width=200 "spring]], oscillates back and forth. (C–H) are six solutions to the Schrödinger Equation for this situation. The horizontal axis is position, the vertical axis is the real part (blue) or imaginary part (red) of the [[wave function]]. [[Stationary state]]s, or energy eigenstates, which are solutions to the time-independent Schrödinger equation, are shown in C, D, E, F, but not G or H.")
![harmonic oscillator]]. Left: The real part (blue) and imaginary part (red) of the wave function. Right: The [[probability distribution]] of finding the particle with this wave function at a given position. The top two rows are examples of '''[[stationary state]]s''', which correspond to [[standing wave]]s. The bottom row is an example of a state which is ''not'' a stationary state. The right column illustrates why stationary states are called "stationary".](https://commons.wikimedia.org/wiki/Special:FilePath/StationaryStatesAnimation.gif?width=200 "harmonic oscillator]]. Left: The real part (blue) and imaginary part (red) of the wave function. Right: The [[probability distribution]] of finding the particle with this wave function at a given position. The top two rows are examples of '''[[stationary state]]s''', which correspond to [[standing wave]]s. The bottom row is an example of a state which is ''not'' a stationary state. The right column illustrates why stationary states are called \"stationary\".")
PARTIAL DIFFERENTIAL EQUATION DESCRIBING HOW THE QUANTUM STATE OF A NON-RELATIVISTIC PHYSICAL SYSTEM CHANGES WITH TIME
Schrodingers equation; Schroedinger's equation; Schroedinger equation; Schrödinger Wave Equation; Schrodinger's equation; Schrödinger wave equation; Schrödinger's equation; Schrödinger-equation; Schrödinger Equation; Schrödinger's wave equation; TDSE; Time-independent Schrödinger equation; Time-independent Schrodinger equation; Time-independent schrödinger equation; Time-independent schrodinger equation; Schrodinger Equation; Shrodinger equation; Shrodinger's equation; Schroedinger Equation; Sherdinger's equation; Shredinger's equation; Sherdinger equation; Shredinger equation; Schrodinger's wave equation; Schrodinger`s equation; Schrodiner`s equation; Erwin Schrodinger's wave model; Time independent Schrödinger equation; Schroedinger wave equation; Time-independent Schroedinger equation; Schrodinger Wave Equation; Schroedinger Wave Equation; Schroedinger's wave equation; Time independent Schroedinger equation; Schrodinger-equation; Time independent Schrodinger equation; Time-independent schroedinger equation; Schroedinger-equation; Schrodinger wave equation; Schrodinger equation; TISE; Schrodinger operator; Schrödinger’s equation; Schrodinger's Wave Equation; Schrödinger's Wave Equation; Schrodinger's Equation; Schrödinger's Equation; Schrodinger model; Schrödinger model; Non-Relativistic Schrodinger Wave Equation; Time-dependent Schrödinger equation; Schrodinger’s equation; Schrodenger equation
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the subject.
