Quantum Mechanics: Dirac Notation and Wavefunction Normalization

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Questions and Answers

How would you define Dirac notation?

  • A notation for expressing mathematical functions in quantum mechanics
  • A notation for solving differential equations in quantum mechanics
  • A notation for representing quantum states using kets and bras (correct)
  • A notation for calculating the position of a particle in quantum mechanics

What is the condition for two kets to be orthonormal?

  • The scalar product of their complex conjugates is 1
  • Their scalar product is 0
  • Their norm is 0
  • The norm of their product is real and positive (correct)

What is the property of the scalar product of two kets?

  • It is commutative
  • It is equal to the product of their complex conjugates (correct)
  • It is always 0
  • It is distributive

How do you normalize a wavefunction?

<p>By making the norm of the wavefunction real and positive (C)</p> Signup and view all the answers

What is the norm of the state ȁ𝜓ۧ = 3𝜙1 − 7𝜙2?

<p>10 (B)</p> Signup and view all the answers

What is the normalization constant if the state ȁ𝜓ۧ = 3𝜙1 − 7𝜙2 is not normalized?

<p>$\sqrt{10}$ (B)</p> Signup and view all the answers

In Dirac notation, what is the orthornormal condition?

<p>$\langle 𝜙_1|𝜙_1 \rangle = 1$, $\langle 𝜙_2|𝜙_2 \rangle = 1$ (D)</p> Signup and view all the answers

How do you normalize a wavefunction?

<p>Divide by its norm (B)</p> Signup and view all the answers

What is the orthonormal condition for two kets 𝜓 and 𝜑?

<p>𝜓 𝜓ۧ = 1 and 𝜑 𝜑ۧ = 1 (B)</p> Signup and view all the answers

In Dirac notation, what does the condition 𝜓 𝜑ۧ = 0 represent?

<p>Orthogonal states (C)</p> Signup and view all the answers

How is the norm of a wavefunction 𝜓 represented in Dirac notation?

<p>𝜓 𝜓ۧ (C)</p> Signup and view all the answers

What is the complex conjugate of a wavefunction in one dimension represented as in Dirac notation?

<p>∫(𝜙 ( x, t )𝝍 * ( x, t ))dx (D)</p> Signup and view all the answers

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