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In a text I am using (Atomic Physics, by Christopher Foot), it states that an atom in a magnetic field can be modeled as a simple harmonic oscillator. I am assuming that there is periodic motion, possibly circular, which makes this a good candidate to be modeled as a simple harmonic oscillator.

The book states the following:

An atom in a magnetic field can be modelled as a simple harmonic oscillator. The restoring force on the electron is the same for displacements in all direction and the oscillator has the same resonant frequency $\omega_0$ for motion along the $x$-, $y$- and $z$- directions (when there is no magnetic field). In a magnetic field $\vec{B}$ the equation of motion for an electron with charge $-e$, position $\vec{r}$ and velocity $\vec{v} = \dot{r}$ is  $$m_e\frac{d\vec{v}}{dt} = -m_e \omega_0^2 \vec{r} - e \vec{v} \times \vec{B}$$

(Relevant page.)

Does anyone have a good geometric interpretation of how how an atom in a magnetic field resembles the motion of a simple harmonic oscillator? Do I have the right idea in assuming that they are implying that in the absence of the magnetic field the electron can be modeled as if it is a simple harmonic oscillator $$m_e\frac{d\vec{v}}{dt} = -m_e \omega_0^2 \vec{r},$$ where the electron would be moving around as if on the surface of a sphere, and this is what is being modeled as a simple harmonic oscillator?

In a text I am using (Atomic Physics, by Christopher Foot), it states that an atom in a magnetic field can be modeled as a simple harmonic oscillator. I am assuming that there is periodic motion, possibly circular, which makes this a good candidate to be modeled as a simple harmonic oscillator.

The book states the following:

An atom in a magnetic field can be modelled as a simple harmonic oscillator. The restoring force on the electron is the same for displacements in all direction and the oscillator has the same resonant frequency $\omega_0$ for motion along the $x$-, $y$- and $z$- directions (when there is no magnetic field). In a magnetic field $\vec{B}$ the equation of motion for an electron with charge $-e$, position $\vec{r}$ and velocity $\vec{v} = \dot{\vec r}$ is  $$m_e\frac{d\vec{v}}{dt} = -m_e \omega_0^2 \vec{r} - e \vec{v} \times \vec{B}$$

(Relevant page.)

Does anyone have a good geometric interpretation of how how an atom in a magnetic field resembles the motion of a simple harmonic oscillator? Do I have the right idea in assuming that they are implying that in the absence of the magnetic field the electron can be modeled as if it is a simple harmonic oscillator $$m_e\frac{d\vec{v}}{dt} = -m_e \omega_0^2 \vec{r},$$ where the electron would be moving around as if on the surface of a sphere, and this is what is being modeled as a simple harmonic oscillator?

In a text I am using, it states that an atom in a magnetic field can be modeled using a simple harmonic oscillator. I am assuming that there is periodic motion, possibly circular, which makes this a good candidate to be modeled as a simple harmonic oscillator. It states the following: "An atom in a magnetic field can be modelled as a simple harmonic oscillator. The restoring force on the electron is the same for displacements in all direction and the oscilator has the same resonant frequency $\omega_0$ for motion along the $x$-, $y$- and $z$- directions (when there is no magnetic field). In a magnetic field $\vec{B}$ the equation of motion for an electron with charge $-e$, position $\vec{r}$ and velocity $\vec{v} = \dot{r}$ is $$m_e\frac{d\vec{v}}{dt} = -m_e \omega_0^2 \vec{r} - e \vec{v} \times \vec{B}$$"

Does anyone have a good geometric interpretation of how how an atom in a magnetic field resembles the motion of a simple harmonic oscillator? Do I have the right idea in assuming that they are implying that in the absence of the magnetic field the electron can be modeled as if it is a simple harmonic oscillator $$m_e\frac{d\vec{v}}{dt} = -m_e \omega_0^2 \vec{r}$$ where electron would be moving around as if on the surface of a sphere, and this is what is being modeled as a simple harmonic oscillator?

Thanks.

In a text I am using (Atomic Physics, by Christopher Foot), it states that an atom in a magnetic field can be modeled as a simple harmonic oscillator. I am assuming that there is periodic motion, possibly circular, which makes this a good candidate to be modeled as a simple harmonic oscillator.

The book states the following:

An atom in a magnetic field can be modelled as a simple harmonic oscillator. The restoring force on the electron is the same for displacements in all direction and the oscillator has the same resonant frequency $\omega_0$ for motion along the $x$-, $y$- and $z$- directions (when there is no magnetic field). In a magnetic field $\vec{B}$ the equation of motion for an electron with charge $-e$, position $\vec{r}$ and velocity $\vec{v} = \dot{r}$ is $$m_e\frac{d\vec{v}}{dt} = -m_e \omega_0^2 \vec{r} - e \vec{v} \times \vec{B}$$

(Relevant page.)

Does anyone have a good geometric interpretation of how how an atom in a magnetic field resembles the motion of a simple harmonic oscillator? Do I have the right idea in assuming that they are implying that in the absence of the magnetic field the electron can be modeled as if it is a simple harmonic oscillator $$m_e\frac{d\vec{v}}{dt} = -m_e \omega_0^2 \vec{r},$$ where the electron would be moving around as if on the surface of a sphere, and this is what is being modeled as a simple harmonic oscillator?

In a text I am using, it states that an atom in a magnetic field can be modeled using a simple harmonic oscillator. I am assuming that there is periodic motion, possibly circular, which makes this a good candidate to be modeled as a simple harmonic oscillator. Does anyone have a good geometric interpretation of how how an atom in a magnetic field resembles the motion of a simple harmonic oscillator?

Thanks.

In a text I am using, it states that an atom in a magnetic field can be modeled using a simple harmonic oscillator. I am assuming that there is periodic motion, possibly circular, which makes this a good candidate to be modeled as a simple harmonic oscillator. It states the following: "An atom in a magnetic field can be modelled as a simple harmonic oscillator. The restoring force on the electron is the same for displacements in all direction and the oscilator has the same resonant frequency $\omega_0$ for motion along the $x$-, $y$- and $z$- directions (when there is no magnetic field). In a magnetic field $\vec{B}$ the equation of motion for an electron with charge $-e$, position $\vec{r}$ and velocity $\vec{v} = \dot{r}$ is $$m_e\frac{d\vec{v}}{dt} = -m_e \omega_0^2 \vec{r} - e \vec{v} \times \vec{B}$$"

Does anyone have a good geometric interpretation of how how an atom in a magnetic field resembles the motion of a simple harmonic oscillator? Do I have the right idea in assuming that they are implying that in the absence of the magnetic field the electron can be modeled as if it is a simple harmonic oscillator $$m_e\frac{d\vec{v}}{dt} = -m_e \omega_0^2 \vec{r}$$ where electron would be moving around as if on the surface of a sphere, and this is what is being modeled as a simple harmonic oscillator?

Thanks.