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At least complex energy and imaginary time are used in quantum mechanics. Complex energy to describe non-stationary processes. Imaginary time is used in Landau Lifshits’s book, Volume 3, Problem 3 to paragraph 77. At the same time, such words are used: “The imaginary value of a moment in time $\tau_0$ corresponds to the classical impracticability of the process” $$W=\exp\left[-2\mathrm{Im}\left(\int_{\tau}^{\tau_0}\frac{4F^2}{\Omega^2}\sin^2\Omega u\mathrm{d}u+\tau_0\right)\right]$$ But to use the complex eigenvalues of quantum mechanics operators, it is necessary to use non-self-adjoint operators, and then the eigenvalues can turn out to be complex. In complex space, the energy and momentum operators are general operators, non-self-adjoint. $$\hat H=\sum_{k=1}^3 -\frac{\hbar^2}{2m}\frac{\partial^2 }{\partial z_k^2},z_k=\mathrm{Re}\,z_k+i \mathrm{Im}\,z_k$$ $$\hat p_r=-i\hbar(\frac{\partial }{\partial r}+\frac{1}{r})$$ The eigenfunction of the radial part of the momentum operator in three-dimensional space is equal to $\psi=exp(ip_r r/\hbar)/r$. The eigenvalues of these operators can be complex. We need to think about the physical meaning of the complex solution. In hydrodynamics, the physical meaning of the imaginary part is the standard deviation. In quantum mechanics, apparently also. You need to measure the constant term described by the real part and the variable one, the fading away term described by the imaginary part. Complex energy and momentum describes the localization in time and in space, respectively, energy and momentum. The imaginary part of the complex energy value is determined from the lifetime of the system. The imaginary part of the impulse is determined from the known complex value of the energy and equations $E^2=p^2c^2+m^2c^4$.

At least complex energy and imaginary time are used in quantum mechanics. Complex energy to describe non-stationary processes. Imaginary time is used in Landau Lifshits’s book, Volume 3, Problem 3 to paragraph 77. At the same time, such words are used: “The imaginary value of a moment in time $\tau_0$ corresponds to the classical impracticability of the process” $$W=\exp\left[-2\mathrm{Im}\left(\int_{\tau}^{\tau_0}\frac{4F^2}{\Omega^2}\sin^2\Omega u\mathrm{d}u+\tau_0\right)\right]$$ But to use the complex eigenvalues of quantum mechanics operators, it is necessary to use non-self-adjoint operators, and then the eigenvalues can turn out to be complex. In complex space, the energy and momentum operators are general operators, non-self-adjoint. $$\hat H=\sum_{k=1}^3 -\frac{\hbar^2}{2m}\frac{\partial^2 }{\partial z_k^2},z_k=\mathrm{Re}\,z_k+i \mathrm{Im}\,z_k$$ $$\hat p_r=-i\hbar(\frac{\partial }{\partial r}+\frac{1}{r})$$ The eigenfunction of the radial part of the momentum operator in three-dimensional space is equal to $\psi=exp(ip_r r/\hbar)/r$. The eigenvalues of these operators can be complex. When writing a solution for the wave function in the complex plane there is a problem. When using real space, there is a non-damping solution only with real coordinates. Similarly, in a complex plane with a complex eigenvalue, a non-damping solution exists at a certain phase of the complex coordinate. We need to think about the physical meaning of the complex solution. In hydrodynamics, the physical meaning of the imaginary part is the standard deviation. In quantum mechanics, apparently also. You need to measure the constant term described by the real part and the variable one, the fading away term described by the imaginary part. Complex energy and momentum describes the localization in time and in space, respectively, energy and momentum. The imaginary part of the complex energy value is determined from the lifetime of the system. The imaginary part of the impulse is determined from the known complex value of the energy and equations $E^2=p^2c^2+m^2c^4$.

At least complex energy and imaginary time are used in quantum mechanics. Complex energy to describe non-stationary processes. Imaginary time is used in Landau Lifshits’s book, Volume 3, Problem 3 to paragraph 77. At the same time, such words are used: “The imaginary value of a moment in time $\tau_0$ corresponds to the classical impracticability of the process” $$W=exp[-2Im(\int_{\tau}^{\tau_0}\frac{4F^2}{\Omega^2}sin^2\Omega udu+\tau_0)]$$ But to use the complex eigenvalues of quantum mechanics operators, it is necessary to use non-self-adjoint operators, and then the eigenvalues can turn out to be complex. In complex space, the energy and momentum operators are general operators, non-self-adjoint. $$\hat H=\sum_{k=1}^3 -\frac{\hbar^2}{2m}\frac{\partial^2 }{\partial z_k^2},z_k=Re z_k+i Im z_k$$ $$\hat p_r=-i\hbar(\frac{\partial }{\partial r}+\frac{1}{r})$$ The eigenfunction of the radial part of the momentum operator in three-dimensional space is equal to $\psi=exp(ip_r r/\hbar)/r$. The eigenvalues of these operators can be complex. We need to think about the physical meaning of the complex solution. In hydrodynamics, the physical meaning of the imaginary part is the standard deviation. In quantum mechanics, apparently also. You need to measure the constant term described by the real part and the variable one, the fading away term described by the imaginary part. Complex energy and momentum describes the localization in time and in space, respectively, energy and momentum. The imaginary part of the complex energy value is determined from the lifetime of the system. The imaginary part of the impulse is determined from the known complex value of the energy and equations $E^2=p^2c^2+m^2c^4$.

At least complex energy and imaginary time are used in quantum mechanics. Complex energy to describe non-stationary processes. Imaginary time is used in Landau Lifshits’s book, Volume 3, Problem 3 to paragraph 77. At the same time, such words are used: “The imaginary value of a moment in time $\tau_0$ corresponds to the classical impracticability of the process” $$W=\exp\left[-2\mathrm{Im}\left(\int_{\tau}^{\tau_0}\frac{4F^2}{\Omega^2}\sin^2\Omega u\mathrm{d}u+\tau_0\right)\right]$$ But to use the complex eigenvalues of quantum mechanics operators, it is necessary to use non-self-adjoint operators, and then the eigenvalues can turn out to be complex. In complex space, the energy and momentum operators are general operators, non-self-adjoint. $$\hat H=\sum_{k=1}^3 -\frac{\hbar^2}{2m}\frac{\partial^2 }{\partial z_k^2},z_k=\mathrm{Re}\,z_k+i \mathrm{Im}\,z_k$$ $$\hat p_r=-i\hbar(\frac{\partial }{\partial r}+\frac{1}{r})$$ The eigenfunction of the radial part of the momentum operator in three-dimensional space is equal to $\psi=exp(ip_r r/\hbar)/r$. The eigenvalues of these operators can be complex. We need to think about the physical meaning of the complex solution. In hydrodynamics, the physical meaning of the imaginary part is the standard deviation. In quantum mechanics, apparently also. You need to measure the constant term described by the real part and the variable one, the fading away term described by the imaginary part. Complex energy and momentum describes the localization in time and in space, respectively, energy and momentum. The imaginary part of the complex energy value is determined from the lifetime of the system. The imaginary part of the impulse is determined from the known complex value of the energy and equations $E^2=p^2c^2+m^2c^4$.

At least complex energy and imaginary time are used in quantum mechanics. Complex energy to describe non-stationary processes. Imaginary time is used in Landau Lifshits’s book, Volume 3, Problem 3 to paragraph 77. At the same time, such words are used: “The imaginary value of a moment in time $\tau_0$ corresponds to the classical impracticability of the process” $$W=exp[-2Im(\int_{\tau}^{\tau_0}\frac{4F^2}{\Omega^2}sin^2\Omega udu+\tau_0)]$$ But to use the complex eigenvalues of quantum mechanics operators, it is necessary to use non-self-adjoint operators, and then the eigenvalues can turn out to be complex. In complex space, the energy and momentum operators are general operators, non-self-adjoint. $$\hat H=\sum_{k=1}^3 -\frac{\hbar^2}{2m}\frac{\partial^2 }{\partial z_k^2},z_k=Re z_k+i Im z_k$$ $$\hat p_r=-i\hbar(\frac{\partial }{\partial r}+\frac{1}{r})$$ The eigenfunction of the momentum operator in three-dimensional space is equal to $\psi=exp(ip_r r/\hbar)/r$. The eigenvalues of these operators can be complex. We need to think about the physical meaning of the complex solution. In hydrodynamics, the physical meaning of the imaginary part is the standard deviation. In quantum mechanics, apparently also. You need to measure the constant term described by the real part and the variable one, the fading away term described by the imaginary part. Complex energy and momentum describes the localization in time and in space, respectively, energy and momentum. The imaginary part of the complex energy value is determined from the lifetime of the system. The imaginary part of the impulse is determined from the known complex value of the energy and equations $E^2=p^2c^2+m^2c^4$.

At least complex energy and imaginary time are used in quantum mechanics. Complex energy to describe non-stationary processes. Imaginary time is used in Landau Lifshits’s book, Volume 3, Problem 3 to paragraph 77. At the same time, such words are used: “The imaginary value of a moment in time $\tau_0$ corresponds to the classical impracticability of the process” $$W=exp[-2Im(\int_{\tau}^{\tau_0}\frac{4F^2}{\Omega^2}sin^2\Omega udu+\tau_0)]$$ But to use the complex eigenvalues of quantum mechanics operators, it is necessary to use non-self-adjoint operators, and then the eigenvalues can turn out to be complex. In complex space, the energy and momentum operators are general operators, non-self-adjoint. $$\hat H=\sum_{k=1}^3 -\frac{\hbar^2}{2m}\frac{\partial^2 }{\partial z_k^2},z_k=Re z_k+i Im z_k$$ $$\hat p_r=-i\hbar(\frac{\partial }{\partial r}+\frac{1}{r})$$ The eigenfunction of the radial part of the momentum operator in three-dimensional space is equal to $\psi=exp(ip_r r/\hbar)/r$. The eigenvalues of these operators can be complex. We need to think about the physical meaning of the complex solution. In hydrodynamics, the physical meaning of the imaginary part is the standard deviation. In quantum mechanics, apparently also. You need to measure the constant term described by the real part and the variable one, the fading away term described by the imaginary part. Complex energy and momentum describes the localization in time and in space, respectively, energy and momentum. The imaginary part of the complex energy value is determined from the lifetime of the system. The imaginary part of the impulse is determined from the known complex value of the energy and equations $E^2=p^2c^2+m^2c^4$.