Table of Contents
Why must a wavefunction be single valued?
The wave function must be single valued. This means that for any given values of x and t , Ψ(x,t) must have a unique value. This is a way of guaranteeing that there is only a single value for the probability of the system being in a given state.
What are the conditions which an eigenfunction must satisfy?
Just as in the case of a stretched string, the Eigen functions of the Schrodinger equation will be those which must satisfy the following conditions: (i) must be single valued and finite i.e., for each value of the variables x.y.z there is only one definite value of the function .
How do you normalize eigenfunctions?
Depending on whether the spectrum is discrete or continuous, the eigenfunctions can be normalized by setting the inner product of the eigenfunctions equal to either a Kronecker delta or a Dirac delta function, respectively.
Is the wave function single valued?
The wavefunction is this case is single-valued.
What is the significance of particle in a box solution?
Introduction. The particle in a box problem is a common application of a quantum mechanical model to a simplified system consisting of a particle moving horizontally within an infinitely deep well from which it cannot escape. The solutions to the problem give possible values of E and ψ that the particle can possess.
What does single valued mean?
Definition of single-valued : having one and only one value of the range associated with each value of the domain a single-valued function — compare multiple-valued.
What are eigenfunctions and eigen values?
The function is called an eigenfunction, and the resulting numerical value is called the eigenvalue. The value of the observable for the system is the eigenvalue, and the system is said to be in an eigenstate.
What are eigenfunctions and eigenvalues in chemistry?
An eigenfunction of an operator is a function such that the application of on gives. again, times a constant. (49) where k is a constant called the eigenvalue. It is easy to show that if is a linear operator with an eigenfunction , then any multiple of is also an eigenfunction of .
Why should wave function be continuous?
(3) The wave function must be continuous everywhere. That is, there are no sudden jumps in the probability density when moving through space. If a function has a discontinuity such as a sharp step upwards or downwards, this can be seen as a limiting case of a very rapid change in the function.
What is the potential function for particle in one dimensional box?
The potential energy is 0 inside the box (V=0 for 0 and goes to infinity at the walls of the box (V=∞ for x<0 or x>L). We assume the walls have infinite potential energy to ensure that the particle has zero probability of being at the walls or outside the box.
What is the physical significance of wave function and ψ2?
ψ is a wave function and refers to the amplitude of electron wave i.e. probability amplitude. It has got no physical significance. [ψ]2 is known as probability density and determines the probability of finding an electron at a point within the atom.