Month: March 2020

In our previous post Position Operator: From Ket vectors to wavefunctions we have seen that wavefunctions are the scalar product of ket vectors with position eigenkets. More precisely we call these position space wavefunctions. We can also have momentum space wavefunctions which are the scalar product of the ket vectors with momentum operator eigenkets. We… Continue reading

A particle in a box of length $latex L&s=2$ is in the state $latex \left|\psi\right\rangle&s=2$ such that its wavefunction is $latex \psi(x)=\left\langle x|\psi\right\rangle= \sqrt{\frac{2}{L}}\sin\left(\frac{\pi x}{L} \right)&s=2$ What is the probability that the particle is in right half of the box? Solution The probability density associated with the given wave function is $latex \mathrm{p}(x) = |\psi(x)|^2=… Continue reading

Suppose we are interested in measuring the position of a quantum particle. The observable that will do the job is the position operator. The eigenvalue equation for position operator is $latex \hat x \left|x\right\rangle=x \left|x\right\rangle&s=2$ Here $latex \left|x\right\rangle &s=2$ are position eigenkets and $latex x &s=2$ are the corresponding eigenvalues. This operator is different from… Continue reading

In A Particle in a Box- 1 we have seen that we can write the quantum state of a particle in a box in the eigen-basis of energy operator. From now on we will call this the Hamiltonian operator. For a recap the eigenvalue equation for the Hamiltonian for a particle in a box system… Continue reading

Here is a short summary of what we have learned. Quantum mechanics is a theory that allows us to calculate the probabilities of fundamental interactions taking place in the microscopic world of atoms and molecules. To calculate these probabilities, and to use quantum mechanics we consider the state of the system which is a vector… Continue reading