12 Questions
How would you define Dirac notation?
A notation for representing quantum states using kets and bras
What is the condition for two kets to be orthonormal?
The norm of their product is real and positive
What is the property of the scalar product of two kets?
It is equal to the product of their complex conjugates
How do you normalize a wavefunction?
By making the norm of the wavefunction real and positive
What is the norm of the state ȁ𝜓ۧ = 3𝜙1 − 7𝜙2?
10
What is the normalization constant if the state ȁ𝜓ۧ = 3𝜙1 − 7𝜙2 is not normalized?
$\sqrt{10}$
In Dirac notation, what is the orthornormal condition?
$\langle 𝜙_1|𝜙_1 \rangle = 1$, $\langle 𝜙_2|𝜙_2 \rangle = 1$
How do you normalize a wavefunction?
Divide by its norm
What is the orthonormal condition for two kets 𝜓 and 𝜑?
𝜓 𝜓ۧ = 1 and 𝜑 𝜑ۧ = 1
In Dirac notation, what does the condition 𝜓 𝜑ۧ = 0 represent?
Orthogonal states
How is the norm of a wavefunction 𝜓 represented in Dirac notation?
𝜓 𝜓ۧ
What is the complex conjugate of a wavefunction in one dimension represented as in Dirac notation?
∫(𝜙 ( x, t )𝝍 * ( x, t ))dx
This quiz covers the definition of Dirac notations in quantum mechanics, as well as the orthonormal condition and the process of normalizing a wavefunction. It is based on Chapter 2 'Mathematical Tools of Quantum Mechanics' by Dr. Wajood Diery, and explores the properties of kets, bras, and bra-kets.
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