0
How do you show that a wave function is a solution to the time- independent Schrodinger equation for a simple harmonic oscillator?
Wiki User
∙ 12y ago
You should substitute your solution in the equation. If the solution is correct you will receive equality. Otherwise your solution is wrong.
Wiki User
∙ 12y ago
To show that a wave function is a solution to the time-independent Schrödinger equation for a simple harmonic oscillator, you substitute the wave function into the Schrödinger equation and simplify. This will involve applying the Hamiltonian operator to the wave function and confirming that it equals a constant times the wave function.
Add your answer:
Earn +20 pts
Wave function for time independent harmonic oscillator?
The wave function for a time-independent harmonic oscillator can be expressed in terms of Hermite polynomials and Gaussian functions. It takes the form of the product of a Gaussian function and a Hermite polynomial, and describes the probability amplitude for finding the oscillator in a particular state. The solutions to the Schrödinger equation for the harmonic oscillator exhibit quantized energy levels, known as energy eigenstates.
Who determined probability location of electrons in atoms?
The probability of finding electrons in an atom is determined by the Schrödinger equation, a fundamental equation of quantum mechanics. This equation describes the wave function of the electron, from which the probability density of finding the electron in a particular region of space can be calculated.
The atom of Erwin Schrodinger and Louis de B oglie?
Erwin Schrodinger is known for his Schrodinger equation, which describes how the wave function of a physical system changes over time. Louis de Broglie proposed the concept of wave-particle duality, suggesting that particles like electrons can exhibit wave-like properties. Both of these contributions were instrumental in the development of quantum mechanics.
How will you calculate potential if the wave function is given?
The potential can be calculated from the wave function using the Schrödinger equation, where the potential energy operator acts on the wave function. This involves solving the time-independent Schrödinger equation to find the potential energy function that corresponds to the given wave function. The potential can be obtained by isolating the potential energy term on one side of the equation.
What is Edwin Schrodinger's wave equation used to calculate?
Schrödinger's wave equation is used to calculate the wave function of a quantum system, which describes the probability distribution of finding a particle in a given state. This equation is an essential tool in quantum mechanics for predicting the behavior of particles at the microscopic scale.
Wave function for time independent harmonic oscillator?
The wave function for a time-independent harmonic oscillator can be expressed in terms of Hermite polynomials and Gaussian functions. It takes the form of the product of a Gaussian function and a Hermite polynomial, and describes the probability amplitude for finding the oscillator in a particular state. The solutions to the Schrödinger equation for the harmonic oscillator exhibit quantized energy levels, known as energy eigenstates.
What is more general between Schrodinger time independent or time dependent wave equation?
The time-independent Schrödinger equation is more general as it describes the stationary states of a quantum system, while the time-dependent Schrödinger equation describes the time evolution of the wave function. The time-independent equation can be derived from the time-dependent equation in specific situations.
How do you convert DC to AC in an oscillator?
that is the function of the oscillator
What is the physical interpretation of bessel function?
spherical bessel function arise in the solution of spherical schrodinger wave equation. in solving the problem of quantum mechanics involving spherical symmetry, like spherical potential well, the solution that is the wave function is spherical bessel function
The atom of Erwin Schrodinger and Louis de B oglie?
Erwin Schrodinger is known for his Schrodinger equation, which describes how the wave function of a physical system changes over time. Louis de Broglie proposed the concept of wave-particle duality, suggesting that particles like electrons can exhibit wave-like properties. Both of these contributions were instrumental in the development of quantum mechanics.
What evidence did Erwin Schrodinger have to support is theory?
Erwin Schrödinger developed his theory of wave mechanics to explain the behavior of electrons in atoms. His theory was supported by the successful explanation of the spectrum of hydrogen atoms and the ability to calculate various properties of atoms based on the wave function. Additionally, experimental evidence, such as diffraction patterns of electrons, provided support for his wave-particle duality concept.
Can solve the harmonic oscillator expectation value?
The expectation value of an operator in the harmonic oscillator can be calculated by using the wave functions (eigenfunctions) of the harmonic oscillator and the corresponding eigenvalues (energies). The expectation value of an operator A is given by the integral of the product of the wave function and the operator applied to the wave function, squared, integrated over all space.
What are the independent variables of a function?
An independent variable of a function is the variable that you cannot change by changing the other. Changes to it are not caused by the equation. If you want to graph how the money you invest in a bank account against the time that the money has been in the account, time is the independent variable. This is because the time will change at a constant rate, no matter how much or how often the money collects interest. If you change the equation, the money earned will change, but the time will not.
What is Edwin Schrodinger's wave equation used to calculate?
Schrödinger's wave equation is used to calculate the wave function of a quantum system, which describes the probability distribution of finding a particle in a given state. This equation is an essential tool in quantum mechanics for predicting the behavior of particles at the microscopic scale.
In the equation V equals πr 3 the volume of a sphere V is a function of R the spheres radius. What is the independent quantity in this function?
The volume of a sphere = 4/3*pi*radius3
Derive schrodinger wave equation?
The Schrödinger wave equation describes how the quantum state of a system evolves over time. It is obtained by applying the principles of quantum mechanics to a system's wave function, resulting in a differential equation that describes how the wave function changes in time. The equation is named after physicist Erwin Schrödinger who originally formulated it in 1926.
Is this equation a function y equals 3squared plus 2x minus 3 is this a function?
You can tell if an equation is a function if for any x value that you put into the function, you get only one y value. The equation you asked about is the equation of a line. It is a function.
