# Tagged Questions

The term "harmonic oscillator" is used to describe any system with a "linear" restoring force that tends to return the system to a equilibrium state. There is both a classical harmonic oscillator and a quantum harmonic oscillator. Both are used to as toy problems that describe many physical systems.

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### Quantum mechanics: SHM expectation of $x^2$ time independent for one state but not superposition of 2 states?

my answers for the first bits $$\langle H\rangle =n\hbar\omega$$ $$\langle x\rangle =\sqrt\frac{\hbar n}{2m\omega}\cos(\omega t)$$ $$\langle p\rangle =-\sqrt\frac{\hbar m\omega n}{2}\sin(\omega t)$$ ...
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### Hamiltonian of a quantum harmonic oscillator

On page 286-287 of Nielsen Chuang's Quantum Information and Quantum Computation (10th edition) book, the Hamiltonian for a quantum harmonic oscillator is approximated as $H=a^\dagger a.$ What are the ...
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### Frequency of driven damped oscillation and the driven force

For a driven damped oscillation, if the driven force $F = F_0 \cos(\omega t)$, then the solution to the motion is $$x = A \cos(\omega t+\varphi ) \, .$$ Why must the the oscillation and the driven ...
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### Can a uniform circular motion be considered as simple harmonic motion? [duplicate]

The acceleration in a circular motion is directed towards the centre and is directly proportional to the radius of circle if it has uniform angular velocity. Is circular motion with uniform angular ...
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### Oscillating block amplitude change when 2nd mass added [closed]

There is a oscillating block with amplitude $A$ and mass $M$. We add a mass $m$ with zero velocity and vertically.when the block is in this two conditions: ...
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### Birkhoff Method for Harmonic Oscillator Perturbation

Problem: Given Hamiltonian $$H = \frac12 (p^{2}+q^{2})+q^{3}-3qp^{2}$$ make a perturbative canonical transformation $(q,p) \rightarrow (Q,P)$ such that the new Hamiltonian, apart from terms of degree ...
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### Simple Harmonic Motion Derivatives, and the equation

If the velocity time graph of a SHM is the derivative of the Distance time graph, and the kinetic energy of the mass in the SHM is maximum when the displacement is 0, how can the maximum velocity be ...
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### The “general uncertainty” of the harmonic oscillator defies the correspondence principle?

If you use the definition of $(\Delta x)^2 = \langle n | x^2 | n \rangle - \langle n | x | n \rangle^2$ and the same for $(\Delta p)^2$ to calculate $\Delta x \Delta p$ for the state $|n\rangle$ of a ...
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### Do you know the principle which says that connecting two sources of similar kind produces a waste and destruction? [closed]

There is a great article, called commutation cells, which states that you cannot transfer kinetic energy from one container to another immediately, bypassing the potential energy storage. Otherwise, ...
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### Why $k/m$ in simple Harmonic motion equal $\omega^2$? [closed]

I've come across this thing in simple harmonic motion but never did I manage to find a reason why $k/m$ should equal $\omega^2$ and the theory behind it. People say it is done for convenience equating ...
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### Why are harmonic oscillators quantized? [closed]

What physical reason is there for a mass on a spring to have discrete energy levels? And why are those energy levels equally spaced, i.e. why is $E \ \alpha \ f$? Personal background and ...
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### I do not understand why $a_-a_+\psi_n=(n+1)\psi_n$ and not $\sqrt n(n+1))\psi_n$ [duplicate]

I do not understand why $a_-a_+\psi_n=(n+1)\psi_n$ and not $\sqrt n(n+1))\psi_n$ or how the Energy formula can help me understand this (I was told that it would). In the introduction to quantum ...
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### I do not understand why $a_-a_+\psi_n=(n+1)\psi_n$

I do not understand why $a_-a_+\psi_n=(n+1)\psi_n$ and not $\sqrt n(n+1))\psi_n$ or how the Energy formula can help me understand this (I was told that it would). In the introduction to quantum ...
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### Quantum harmonic oscillator, clarification about the period

We can write the general state |A> at time $t=0$ as $|A, 0>=\sum a_n |n>$ where |n> are the eigenvectors of the oscillator. In my textbook there is written that if the $a_n=0$ for every n=even ...
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### Resonance of a system featuring a collection of individual resonators?

Suppose you had a number of harmonic oscillators, each with different resonant frequencies in a system. Does this imply that their is an overall system resonance that is dependent on the individual ...
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### Deriving time period of oscillation [closed]

I have attached the question image.
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### Total energy of a simple pendulum proportional to the square of the amplitude? [duplicate]

It is known that in simple harmonic motion, the total energy of the system is proportional the square of the amplitude, but how can I prove that for a simple pendulum where amplitude is the arc length ...
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### Spring-mass system with complex spring constant

Suppose a system containing a mass $m$ on frictionless surface, attached by a spring to a wall. The spring's constant is complex, given by $K = K_1 + K_2i$, with $K_1 \gg K_2$. Write the equation of ...